Question

is it possible for a function to satisfy f(x)>0, f'(x)>0, and f''(x) < 0 on an interval? Explain

Answer 1

yes

Explanation:

In general, the function value, first derivative, and second derivative can be specified independently at a particular point. Their signs can generally be specified independently on some interval.

The function f(x) = 1-x^2 meets your requirements on the interval (-1, 0).