a. find the derivative of f at x. that is, fi...
a. find the derivative of f at x. that is, find f(x). b. find the slope of the tangent line to the graph of f at each of the two values of x given to the right of the function. f(x)= - 3x + 1; x = - 2, x = 4 a. what is the derivative of f(x)= - 3x + 1 at x? f(x)= (simplify your answer.)
Answer
# Explanation:
## Step1: Apply power - rule for derivatives
The power - rule states that if $y = ax^n$, then $y^\prime=anx^{n - 1}$. For the function $f(x)=-3x + 1$, the derivative of $-3x$ is $-3\times1\times x^{1-1}=-3$ (since $a=-3$ and $n = 1$ for the term $-3x$), and the derivative of the constant term $1$ is $0$ (because if $y = c$ where $c$ is a constant, $y^\prime=0$).
$f^\prime(x)=\frac{d}{dx}(-3x)+\frac{d}{dx}(1)$
## Step2: Calculate the derivative
$\frac{d}{dx}(-3x)=-3$ and $\frac{d}{dx}(1)=0$, so $f^\prime(x)=-3$.
# Answer:
$-3$