Question

The graph of y = f ′(x), the derivative of f(x), is shown below. Given f(2) = 8, evaluate f(–2).

Answer 1

Answer:  Third option is correct.

Step-by-step explanation:

Since we have given that

The graph of the derivative of f(x) , say, y = f'(x), is symmetry about the origin.

so, it is an odd function.

So, f(x) must be an even function.

$f(x)=f(-x)\\\\f(2)=f(-2)=8$

So, the value of f(-2) is equal to 8.

Hence, Third option is correct.