Determine the interval(s) at which f(x) is concave up given that f′′(x)=−x2+x+6.
a) (–2, 3)
b) (–∞, –2), (3, ∞)
c) (–∞, –3), (2, ∞)
d) (–2, ∞)
e) (–∞, 3)
-x^2+x+6 = -(x-3)(x+2)
As you know, this is a parabola, opening downward. So, it is positive between the roots: -2 and 3.
So, f(x) is concave up in that interval. So, (a)