Question

Determine the interval(s) at which f(x) is concave down given that f′′(x)=−2x2+6x+8.

Answer 1

f''(x) = -2(x +1)(x -4) so is negative for x < -1 and x > 4

f(x) is concave downward on the intervals (-∞, -1) ∪ (4, ∞).