Question

The graph of y = f ′(x), the derivative of f(x), is shown below. List the intervals where the graph of f is concave down.

(–4, –2) U (2, 4)
(–2, 2)
(–4, 0)
(0, 4)

Answer 1

(a) (–4, –2) U (2, 4)

Explanation:

A graph is concave down where its second derivative is negative. That will be where the slope of the first derivative is negative.

Your graph shows the first derivative has negative slope at the left and right ends. The function f(x) will be concave downward on those intervals:

(–4, –2) U (2, 4)