Let on .…

MATHEMATICS · Single correct · AP · Calculus AB · Differentiation: Composite, Implicit, and Inverse Functions · Differentiation: Composite, Implicit, and Inverse Functions

Problem

Let

f(x)=\int_{\sin x}^{\cos x}e^{t+\sin^{-1}(t)^2}\,dt

on

\left[0,\frac{\pi}{2}\right]

. Then (1)

f''(c)=0

for all

c\in\left(0,\frac{\pi}{2}\right)

(2)

f''(c)=0

for some

c\in\left(0,\frac{\pi}{2}\right)

(3)

f'(c)=0

for some

c\in\left(0,\frac{\pi}{2}\right)

(4)

f(c)\ne0

for all

c\in\left(0,\frac{\pi}{2}\right)

Related theory

Browse the problem library