Question

Determine the interval(s) at which f(x) is concave up given that f′′(x)=−x2+4x+5.

Answer 1

f(x) is concave upward where f''(x) > 0.

f''(x) = -(x -5)(x +1)

This will be greater than 0 for x between the roots of -1 and +5.

f(x) is concave upward on the interval (-1, 5).