For all real

MATHEMATICS · Single correct · AP · Calculus AB · Analytical Applications of Differentiation · Analytical Applications of Differentiation

Problem

For all real xx, let ff be differentiable with f′(x)=(x−1)(x−4)f'(x)=(x-1)(x-4). Define F(x)=∫2xf(t) dtF(x)=\displaystyle\int_{2}^{x} f(t)\,dt. On which interval is FF concave up? (a) (1,4)(1,4) (b) (1,∞)(1,\infty) (c) (−∞,1)∪(4,∞)(-\infty,1)\cup(4,\infty) (d) (52,∞)(\tfrac{5}{2},\infty)

Related theory

Browse the problem library