A differentiable function satisfies f'(x)0 (2<x<4)

MATHEMATICS · Subjective · AP · Calculus AB · Analytical Applications of Differentiation · Analytical Applications of Differentiation

Problem

A differentiable function ff satisfies f′(x)<0(0<x<2),f′(x)>0(2<x<4),f′(x)<0(4<x<6).f'(x)<0\quad (0<x<2),\qquad f'(x)>0\quad (2<x<4),\qquad f'(x)<0\quad (4<x<6). Let F(x)=∫0xf(t) dtF(x)=\int_{0}^{x} f(t)\,dt. Determine all xx in (0,6)(0,6) at which FF has an inflection point.

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