First and Second Derivative Test Question 16

calculator allowed For $-2.5 \lt x \lt 2.5$ , let $f$ be a continous function with first derivative given by $f'(x)=e^{(x^4-2x^2+2)}-4$ . Which of the following are all intervals on which the graph of $f$ is concave down?

(-1.273,-0.615)

and

(0.615, 1.273,)

(-0.615,0.615)

(-2.5,-1)

and

(0,1)

(-1,1)

Approach

The graph of $f$ will be concave down when $f'(x)$ is decreasing.

The graph of $f'$ is shown below. Note that per the question the interval begins at $-2.5$ .