Let on the interval

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

Problem

Let g(x)=tan⁡x−2xg(x)=\tan x-2x on the interval (−π2,π2)\left(-\dfrac{\pi}{2},\dfrac{\pi}{2}\right). On which open subinterval(s) of this domain is gg increasing? (a) (−π2,−π4)\left(-\dfrac{\pi}{2},-\dfrac{\pi}{4}\right) and (π4,π2)\left(\dfrac{\pi}{4},\dfrac{\pi}{2}\right) (b) (−π4,π4)\left(-\dfrac{\pi}{4},\dfrac{\pi}{4}\right) (c) (π4,π2)\left(\dfrac{\pi}{4},\dfrac{\pi}{2}\right) (d) everywhere on (−π2,π2)\left(-\dfrac{\pi}{2},\dfrac{\pi}{2}\right) except at x=0x=0

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