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

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).