Calcul
Limites, dérivées, optimisation et comportement des fonctions.
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a student likes watching television to relax but has to write a big pap…
D. Take a five - minute walk.
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the function ( f(x) ) is represented below as a graph. use ( f(x) ) to …
Blank #1: 5 Blank #2: -3
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let $f(x) = 2x^3 + 15x^2 - 36x + 16$ be defined on $-7, 7$. find: a. th…
s: a. The absolute maximum is at the ordered pair \( \boldsymbol{(7, 1185)} \) b. The absolute minimum is at the ordered pair \( \boldsymbol{(1, -3)} \)
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find the exact location of the relative and absolute extrema of the fun…
- \( g(x) \) has an absolute minimum at \( (x,y) = (3, -32) \) - \( g(x) \) has an absolute maximum at \( (x,y) = (-3, 40) \) - \( g(x) \) has a relative minimum at \( (x,y) = (-1…
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find the exact location of all the relative and absolute extrema of the…
- \( f \) has a relative minimum (and absolute minimum) at \( (x,y)=(1, - 8) \) (smallest \( x \) - value for minimum). - \( f \) has an absolute maximum at \( (x,y)=(3,0) \) (lar…
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find the limit. (in the limit, direct substitution applies? \\(\\lim_{x…
$0$
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consider the function $f(x) = 108x^{1/3} - 4x$ over the domain $0, 140$…
(Part a): Critical values are \( x = 0 \) (classified as a point where the derivative is undefined) and \( x = 27 \) (classified as a point where the derivative is zero). ### Part…
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compositions of functions - the composition of functions is the process…
1. $f(g(x)) = -2x + 8$ 2. $(f \circ g)(x) = -12x - 8$ 3. $g(f(x)) = -2x - 1$ 4. $(g \circ f)(x) = -12x + 7$
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consider the rational function $f(x)=\frac{x^2 - 16}{x - 3}$, whose gra…
B. 4.5
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compute. 2 - 6 - 5
$-9$
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graph $y = 2x + 8$.
The line passes through points $(0, 8)$ and $(-4, 0)$, and extends infinitely in both directions along the grid.
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make a connection consider the graph of the equation $y = mx + b$. a. h…
a. Changing $m$ modifies the line's slope (steepness and direction): larger $|m|$ = steeper line; positive $m$ rises left-to-right, negative $m$ falls left-to-right; $m=0$ gives a…
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y = 10x + 50. a. graph the linear equation.
1. Plot the y-intercept at $(0, 50)$. 2. Plot a second point at $(1, 60)$ (using the slope of 10). 3. Draw a straight line through these two points, extending it across the visibl…
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f(x) = \\begin{cases} -x^2 + 4 & \\text{for } x \\leq 2 \\\\ 4x & \\tex…
The graph consists of: 1. A downward-opening parabola $f(x)=-x^2+4$ for $x\leq2$, with a closed endpoint at $(2, 0)$, passing through $(-2,0)$ and $(0,4)$. 2. A ray of the line $f…
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find (g ∘ f)(x). (g ∘ f)(x) = cot(-8x) choose the correct graph of (g ∘…
D. (The graph with vertical asymptotes spaced $\frac{\pi}{8}$ apart, where the curve increases between consecutive asymptotes)
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question 6, 6.5.47 part 2 of 4 hw score: 62.5%, 5 of 8 points points: 0…
$(f \circ g)(x) = -8\cot x$ Correct graph: A.
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find (f ∘ g)(x) and (g ∘ f)(x) and graph each of these functions. f(x) …
$\boldsymbol{-8\cot x}$
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question 24 $y = -2\\tan(4x - \\pi) - 1$, what is the period of this fu…
b. \( -\frac{\pi}{4} \) ### Second Question (Period of \( y = -2\tan(4x - \pi) - 1 \))
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question 22 $y = -2\\cos(4x + \\pi) - 1$, what is the period of this fu…
a. 2 ### Second Question (Period)
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question 6 consider the function $f(x)=x^2 - 6x + 3$ graph $f(x)$ what …
- Vertex of $f$: $(3, -6)$ - Equation of the line of symmetry: $x=3$ - $f$ has a minimum of $-6$ - The $x$-intercept(s) of $f$ is/are: $(0.55, 0)$ and $(5.45, 0)$ - The $y$-interc…
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the graph of a function is given below. give all x-intercepts and y-int…
(a) \(x\) - intercept(s): \(2\) (b) \(y\) - intercept(s): \(1\) Wait, no, after re - examining the graph, the correct x - intercept is \(2\) (since the graph crosses the x - axis …
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which of the following statements about google photos is false? it can …
The statement "Integration with Facebook and Instagram allows users to add their favorite photos to these social networks with one tap" is false. So the answer is the option with …
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fractions worksheet find the sum. 1. $4\\frac{5}{6} + \\frac{4}{5} =$ 2…
1. $5\frac{19}{30}$ 2. $8\frac{2}{3}$ 3. $4\frac{1}{8}$ 4. $1\frac{17}{20}$ 5. $7\frac{46}{55}$ 6. $1\frac{13}{20}$ 7. $9\frac{2}{63}$ 8. $6\frac{7}{9}$ 9. $9\frac{5}{22}$ 10. $7\…
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if $p(x) = 3x^2 - 2x + 1$, find $p(-4)$.
57
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write the function with the given transformation from the given parent …
$f(x) = -5\sqrt[3]{x} + 7$
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determine whether each description best refers to a sole proprietorship…
To solve this, we analyze each description based on the characteristics of sole proprietorship, partnership, corporation, and LLC: ### Part a - A corporation is a separate legal e…
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given the function $f(x) = 4x^2 - 5x + 4$. calculate the following valu…
$f(-2)=30$ $f(-1)=13$ $f(0)=4$ $f(1)=3$ $f(2)=10$
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write a function in any form that would match the graph shown below.
$y=-\frac{5}{3}(x+3)^2(x-1)(x-2)$
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find the derivative of $f(x) = \\frac{1}{(2x^5 + \\sin x)^3}$.\ \ $\\bi…
$\boldsymbol{f'(x)=\frac{-3(10x^{4}+\cos x)}{(2x^{5}+\sin x)^{4}}}$ (the third option)
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trazar la recta. $y = -\\frac{3}{2}x - 3$
To draw the line \(y =-\frac{3}{2}x-3\), plot the points \((0, - 3)\), \((2,-6)\) (or \((-2,0)\)) and draw a straight line through them.
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problem 14. (1 point) let ( f ) be a differentiable function. suppose t…
\(162\)
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let ( f ) be a twice - differentiable function with first derivative ( …
B. \(5xf(x^{2})-\int 5f(x^{2})dx\)
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differentiate. y = 2x² cos x cot x y =
\(4x\cos x\cot x - 2x^{2}\cos x-2x^{2}\cos x\csc^{2}x\) (or equivalent simplified forms)
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f(x) = -(x + 2)(x - 2)^2(x - 7) plot the y-intercept and the roots. cli…
Roots (x-intercepts): $(-2, 0)$, $(2, 0)$, $(7, 0)$ y-intercept: $(0, 56)$
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find $f(x)$ and $f(x)$ if $f(x) = \\frac{x^2}{x - 3}$. $f(x) = \\square…
\( f'(x)=\frac{x^2 - 6x}{(x - 3)^2} \) \( f''(x)=\frac{18}{(x - 3)^3} \)
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write a function in any form that would match the graph shown below.
$y=-\frac{1}{2}(x+1)(x-4)^2$ (or expanded form $y=-\frac{1}{2}x^3+\frac{7}{2}x^2-4x-8$)
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write a function in any form that would match the graph shown below.
$y=-\frac{1}{5}(x+5)^2(x-1)$
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9. 0 / 1 points let $h(x) = \\frac{f(x)}{1 + g(x)}$. given $f(5) = 1$, …
\( -\frac{1}{4} \)
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write a function in any form that would match the graph shown below.
$y=(x+3)(x-8)$ (or $y=x^2-5x-24$)
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7. 0 / 0.62 points practice another differentiate. \\( y = 4x^2 \\sin x…
\( y' = 8x\sin x\tan x + 4x^2\sin x + 4x^2\sin x\sec^2 x \) (or equivalent simplified forms, e.g., \( y' = 8x\sin x\tan x + 4x^2\sin x(1 + \sec^2 x) \) or further simplified using…
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for each of the following integrals, select the best method to evaluate…
s: 1. For \( \int\frac{3^{(\ln(x))^2}}{x}dx \), the best method is \( \boldsymbol{u} \) - substitution (let \( u = (\ln x)^2 \) or \( u=\ln x \) depending on the intended problem,…
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trazar el gráfico de la recta. -2x + y = -6
To graph the line \(-2x + y=-6\) (or \(y = 2x-6\)): 1. Plot the y - intercept \((0,-6)\). 2. Plot the x - intercept \((3,0)\) (found by setting \(y = 0\) in \(y = 2x-6\) and solvi…
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the solutions to the inequality $y > -3x + 2$ are shaded on the graph. …
B. (2, 0)
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las funciones f y g se definen a continuación. $f(x)=4x - 3$ $g(x)=-4x^…
\( f(-3) = -15 \) \( g(4) = -67 \)
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las funciones f y g se definen a continuación. $f(x) = -3x^3 - 2$ $g(x)…
\( f(-2) = \boldsymbol{22} \) \( g(7) = \boldsymbol{-17} \)
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problem 1. (1 point) for each of the following integrals, select the be…
1. D. $u = \sec(x)$ 2. C. $u=\tan(x)$
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question 29 find the derivative of $y = \\sin(3x^2 - 4x + 1)$. \\(\\fra…
$\frac{dy}{dx}=(6x-4)\cos(3x^2-4x+1)$
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question 28 consider the function $f(x)=\\sqrt3{x}$ near $x = 8$. find …
0.00008
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find the derivative of $g(x) = \\frac{1}{x^7}$.\ \ $g(x) = \\frac{1}{7x…
$g'(x)=-\frac{7}{x^8}$
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all sides of a square are increasing at a rate of 4 centimeters per sec…
$\boldsymbol{\frac{dA}{dt} = 80\frac{\text{cm}^2}{\text{sec}}}$ (corresponding to the second option)
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question 24 let ( f(x) = (12x^2 + 36)^5 ). find the differential, ( df …
$df = 120x(12x^2+36)^4dx$ (the fourth option)
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question 23 use the limit definition of the derivative to find $f(x)$ w…
$f'(x)=14x$
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question 22 write the equation of the line tangent to $f(x)=\\frac{1}{x…
y = -5x + 6
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467\ x36\ \ \ +\ \
Los números para los recuadros son: Primera fila: 2 8 0 2 Segunda fila: 1 4 0 1 Resultado final: $16812$
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question 19 find the derivative of $y = \\arctan(5x^2 - 1)$. \\(\\bolds…
$\boldsymbol{\frac{dy}{dx} = \frac{10x}{25x^4 - 10x^2 + 2}}$ (the third option)
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trazar la recta. y=\\frac{1}{4}x+5
To draw the line \(y=\frac{1}{4}x + 5\), plot the y - intercept \((0,5)\) and use the slope \(\frac{1}{4}\) to find another point (e.g., \((4,6)\) or \((-4,4)\)) and draw a straig…
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question 17 find the derivative of $y = e^{5x}\\cos(3x)$. \\(\\frac{dy}…
$\boldsymbol{\frac{dy}{dx}=5e^{5x}\cos(3x)-3e^{5x}\sin(3x)}$ (corresponding to the third option)
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question 15 find the linear approximation of $f(x)=\\sqrt5{x}$ when $x …
L(x) = -1 + $\frac{1}{5}$(x+1)
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question 14 find the derivative of $f(x) = 3x^5\\sin x + 8\\cos x$. \\(…
$f'(x)=15x^{4}\sin x + 3x^{5}\cos x - 8\sin x$
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trazar la recta. $y = -\\frac{2}{3}x + 1$
To draw the line \(y =-\frac{2}{3}x + 1\), plot the y - intercept \((0,1)\) and use the slope \(-\frac{2}{3}\) to find another point (e.g., \((3,-1)\) or \((-3,3)\)) and then draw…
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find the derivative of $f(x) = \\ln\\left(\\frac{x^6}{2x^5 - 7}\ ight)$…
$f'(x)=\frac{6}{x}-\frac{10x^4}{2x^5 - 7}$
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question 8 find the derivative of $y = \\tan(3^{4x}+1)$. $\\frac{dy}{dx…
$\boldsymbol{\frac{dy}{dx} = 4\cdot 3^{4x}\ln3\cdot \sec^2(3^{4x}+1)}$ (the second option)
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write newton’s formula used to approximate a solution of the equation $…
D. $x_{n+1}=x_n - \frac{2x_n^3 - x_n - 15}{6x_n^2 - 1}; x_3 \approx 2.042527942$
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a sphere is to be designed with a radius of 72 in. use differentials to…
32,572.03 $\text{in}^3$
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determine if the function $f(x)=\\sqrt4{x^3}$ is differentiable at $x =…
$f(x)=\sqrt[4]{x^3}$ is not differentiable at $x = 0$ because $f'(0)$ is not defined.
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what is $f(x) + f(x) + f(x)$? $3f(x)$ complete $3f(x) = 3x^2$ complete …
12
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find the average value of $f(x)=e^{2x}$ over the interval $0, ln 5$. a.…
d.) $\frac{12}{\ln5}$
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if f and g are the functions whose graphs are shown, let u(x) = f(x)g(x…
### Part (a): Find \( u'(1) \) #### Explanation: To find \( u'(1) \) where \( u(x) = f(x)g(x) \), we use the product rule: \( u'(x) = f'(x)g(x) + f(x)g'(x) \). We need to determin…
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write a function in any form that would match the graph shown below. an…
$f(x) = -\frac{125}{24}(x+6)(x+4)(x-8)$
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question write a function in any form that would match the graph shown …
$f(x)=-3(x+4)(x-5)^2$
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tinjiuh bseibhu answer attempt 1 out of 2 $f(x) = \\square$ submit answ…
$5x^2+5x-30$
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solve the integral \\(\\int e^{x}\\sqrt{5e^{x} + 4}\\ dx\\) with the fo…
a.) $\frac{2}{15}(5e^{x}+4)^{\frac{3}{2}}+c$
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$$int \tan^{9}xsec^{2}x dx$$ a.) $\frac{1}{10}\tan^{10}x + c$ b.) $\fra…
a.) $\frac{1}{10}\tan^{10}x + c$
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$$int 18x^3(3x^4 + 7)^9 dx$$ a.) $\frac{9}{5}(3x^4 + 7)^{10}+c$ b.) $\f…
d.) $\frac{3}{20}(3x^4 + 7)^{10}+c$
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$$int (12e^x - 7^x + 7x^5) dx$$ a.) $12e^x + \frac{7^x}{ln 7} + \frac{7…
b.) $12e^{x}-\frac{7^{x}}{\ln7}+\frac{7}{6}x^{6}+c$
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unit 5 — challenge 5.3: antiderivatives use the fundamental theorem of …
c.) $\int_{-2}^{1} 5x^4 dx = 33$
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question 3 of 10 if $f(x) = 3x^2$ and $g(x) = x + 2$, find $(f \\bullet…
D. \( 3x^3 + 6x^2 \)
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Question was provided via image upload.
$3$
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there were 74 ice pops in a freezer. david put additional ice pops in t…
22
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find the intercepts and use them to graph the equation. y=2x+4 select t…
A. The intercept(s) is/are $(-2, 0), (0, 4)$ To graph the line, plot the points $(-2, 0)$ and $(0, 4)$, then draw a straight line connecting them.
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let $f(x) = \\frac{1}{x - 2}$ and $g(x) = 2x + 5$. then $(f \\circ g)(2…
$(f \circ g)(2) = \frac{1}{7}$ $(f \circ g)(x) = \frac{1}{2x+3}$
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f(x) = 8(x - 4)^{2/3} + 8. (a) find the interval(s) where f(x) is incre…
To solve the problem, we analyze the function \( f(x) = 8(x - 4)^{2/3} + 8 \) by examining its derivative. ### Step 1: Find the derivative of \( f(x) \) We use the chain rule. Let…
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given that $f(x) = 2x - 8$ and $g(x) = 2 - x^2$, calculate (a) $f(g(0))…
(a) $-4$ (b) $-62$
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if $f(x) = x^2 + 3$, $g(x) = x - 2$, and $h(x) = \\sqrt{x}$, then $(f \…
$(f \circ g)(x) = x^2 -4x +7$ $(g \circ f)(x) = x^2 +1$ $(h \circ g)(x) = \sqrt{x-2}$
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let $f(x) = \\sqrt{x}$ and $g(x) = \\frac{1}{x + 4}$. find the composit…
$\frac{1}{\sqrt{x+4}}$ (or equivalently $\sqrt{\frac{1}{x+4}}$)
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let $f(x) = x^2 e^{9x}$. (a) find the critical values of $f(x)$. if the…
\( -\frac{2}{9}, 0 \) ### Part (b): Intervals where \( f(x) \) is increasing
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in each part that follows, you are given an equation of a line and a po…
(a) $\boldsymbol{y = -\frac{1}{8}x}$ (b) $\boldsymbol{y = -\frac{1}{5}x + \frac{16}{5}}$
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if $f(-10) = -2$, then the point \\boxed{} is on the graph of $f$. ques…
$(-10, -2)$
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the plot below represents the function $f(x)$: evaluate $f(4)$: $f(4) =…
$f(4) = 1$ $x = 2$
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the plot below represents the function $f(x)$: evaluate $f(4)$: $f(4) =…
$f(4) = 2$ $x = -2$
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question 28 of 50 divide. 13.3 ÷ 0.7 question 29 of 50 david’s annual s…
19 ### Question 29
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for the last 6 days, chiang worked 4.9 hours each day. how many hours d…
0.6 ### Question 24
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attempt 1; 10 attempts remaining. the function \\( f(x) = -6x^3 + 36x^2…
- The function is increasing on the interval \( \boldsymbol{(1, 3)} \). - It is decreasing on the interval \( \boldsymbol{(-\infty, 1)} \) and the interval \( \boldsymbol{(3, \inf…
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produce a rule for the function whose graph is shown. (hint: consider u…
$$ f(x)= \begin{cases} -\dfrac{1}{4}x^2 & \text{for } x < 3 \\ 2 & \text{for } x \geq 3 \end{cases} $$
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produce a rule for the function whose graph is shown. (hint: consider u…
$$ f(x)= \begin{cases} -\sqrt{x} & \text{for } x < 3 \\ 2 & \text{for } x \geq 3 \end{cases} $$
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graph the function. $r(x)=\\begin{cases} x^2 - 1 & \\text{for } x \\leq…
The graph consists of: 1. The left portion: the parabola $y = x^2 - 1$ for all $x \leq 1$, with a closed point at $(1, 0)$. 2. The right portion: the straight line $y = 5x - 5$ fo…
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6.2 symmetry and piecewise - defined functions question 12 of 15 (4 poi…
leftmost, $(1, 0)$
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r(x) = \\begin{cases} x^2 - 1 & \\text{for } x \\leq 1 \\\\ 5x - 5 & \\…
Slope: $5$, y-intercept: $(0, -5)$
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graph the function.\\( r(x) = \\begin{cases} x^2 - 1 & \\text{for } x \…
The solid dot is at $(1, 0)$
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graph the function. $r(x) = \\begin{cases} \\ \\ x^2 - 1\\ \\text{ for …
quadratic function (parabola); $(0, -1)$