Question

Suppose that f is positive, concave upward, and f''(x) exists on an interval I. Show that the function g(x)=[f(x)]^2 is also concave upward on I.

Answer 1

To show the function g(x) is concave up, you need to show \(g''(x)\gt 0\)

Answer 2

\(g(x) = [f(x)]^2 \implies g'(x)=2f(x)f'(x)\)

differentiate again