Let , where is continuous and is differentiable. Explain in one or two sentences how…

MATHEMATICS · Subjective · AP · Calculus AB · Integration and Accumulation of Change · Integration and Accumulation of Change

Problem

Let

g(x)=\displaystyle \int_{3}^{h(x)} f(t)\,dt

, where

f

is continuous and

h

is differentiable. Explain in one or two sentences how the signs of

f\bigl(h(x_0)\bigr)

and

h'(x_0)

together determine whether

g

is increasing or decreasing at

x=x_0