Question

hw9 the derivative as a function (targets l6, d1, d2; §3.2)
score: 5/9 answered: 5/9
question 6
for the function $f(x)=5x^{2}+3x$, evaluate and simplify.
$\frac{f(x + h)-f(x)}{h}=$
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Explanation:

Step1: Find $f(x + h)$

Substitute $x+h$ into $f(x)$:
$f(x + h)=5(x + h)^2+3(x + h)=5(x^{2}+2xh+h^{2})+3x + 3h=5x^{2}+10xh+5h^{2}+3x + 3h$

Step2: Calculate $f(x + h)-f(x)$

$f(x + h)-f(x)=(5x^{2}+10xh+5h^{2}+3x + 3h)-(5x^{2}+3x)=10xh+5h^{2}+3h$

Step3: Calculate $\frac{f(x + h)-f(x)}{h}$

$\frac{f(x + h)-f(x)}{h}=\frac{10xh+5h^{2}+3h}{h}=\frac{h(10x + 5h+3)}{h}=10x + 5h+3$

Answer:

$10x + 5h+3$