Let for . At , which of the following best describes the behavior of…

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

Problem

Let

h(x)=\tan x - 2x

for

0<x<\dfrac{\pi}{2}

. At

x=\dfrac{\pi}{4}

, which of the following best describes the behavior of

h

? (a) Relative maximum because

h''\!\left(\dfrac{\pi}{4}\right)<0

(b) Relative minimum because

h''\!\left(\dfrac{\pi}{4}\right)>0

h''\!\left(\dfrac{\pi}{4}\right)=0

(d) Neither a maximum nor a minimum because

h'\!\left(\dfrac{\pi}{4}\right)\neq 0