Question

let $f$ be the function given by $f(x)=5x^{3}-3x - 7$. what is the value of $f(-2)$?
a -114
b 17
c 50
d 57

Explanation:

Step1: Differentiate the function

Using the power - rule $\frac{d}{dx}(x^n)=nx^{n - 1}$, if $f(x)=5x^{3}-3x - 7$, then $f'(x)=5\times3x^{2}-3=15x^{2}-3$.

Step2: Substitute $x = - 2$

Substitute $x=-2$ into $f'(x)$. So $f'(-2)=15\times(-2)^{2}-3$.
First, calculate $(-2)^{2}=4$. Then $15\times4 - 3=60 - 3=57$.

Answer:

D. 57