Question is down below. Find the t-value at which the graph of h has a point of inflection.

Question

h(t) = −1/3t^3 + 16t^2 + 33t + 172.35, t ≥ 0, and t ≤ 48.

Find the t-value at which the graph of h has a point of inflection.

Answer 1

h(t) = (-1/3)t³ + 16t² +33t + 172.35

h'(t) = -t² + 32t + 33

h"(t) = -2t + 32

h"(t) = 0 when t = 16

If 0 < t < 16, h"(t) > 0, so the graph of h(t) is concave up.

If 16 < t < 48, h"(t) < 0, so the graph of h(t) is concave down

Inflection point is (16, h(16))