Let for . On which of the following intervals is…

MATHEMATICS · Single correct · A Level · Mathematics · Differentiation · Differentiation

Problem

Let

f(x)=\tan x - x

for

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

. On which of the following intervals is

f

increasing? (a)

\left(-\dfrac{\pi}{2},0\right)

only (b)

\left(0,\dfrac{\pi}{2}\right)

only (c)

\left(-\dfrac{\pi}{2},0\right)

and

\left(0,\dfrac{\pi}{2}\right)

(d)

f

is not increasing on any subinterval of

\left(-\dfrac{\pi}{2},\dfrac{\pi}{2}\right)