Question

Use the graph of y=h'(x) below, to estimate point(s) of inflection for the function h(x) , as

well as the intervals on which h(x) is concave up and concave down. Explain your reasoning.

Answer 1

At x = 0 and at x = 2 there are points of inflections. In the intervals of

(negative infinity, 0) and (2, positive infinity) it is concave up.

In the intervals of (0, 2) it is concave down.

Explanation:

Inflection points are point where h'(x) changes from increasing to decreasing and vise versa.

When a graph is concave up, h'(x) is increasing.

When a graph is concave down, h'(x) is decreasing.