Let be a twice–differentiable function such that for and

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

Problem

Let

h

be a twice–differentiable function such that

h'(x)=\sin x

for

0\le x\le 2\pi

and

h(0)=1

. At which value of

x

in the interval

(0,2\pi)

does

h

attain a relative maximum? (a)

x=\dfrac{3\pi}{2}

(b)

x=\pi

(c)

x=2\pi

(d)

x=\dfrac{\pi}{2}