Which statement best describes the monotonic behavior of the function on every open…

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

Problem

Which statement best describes the monotonic behavior of the function

f(x)=\tan x - x

on every open interval between two consecutive vertical asymptotes of

\tan x

? (a)

f

is increasing throughout every such interval. (b)

f

is decreasing throughout every such interval. (c) On each interval

\bigl(-\tfrac{\pi}{2}+k\pi,\;\tfrac{\pi}{2}+k\pi\bigr)

the function increases up to

x=k\pi

and then decreases to the right endpoint. (d) The monotonicity alternates from one interval to the next:

f

is increasing when

k

is even and decreasing when

k

is odd.