Show that f(x) = tan x is an increasing function on (–π/2, π/2). – InterviewSolution

1.

Show that f(x) = tan x is an increasing function on (–π/2, π/2).

Answer»

Given as f(x) = tan x

f'(x) = (d/dx)(tan x)

⇒ f’(x) = sec²x

As given

x ∈ (–π/2, π/2).

That is 4^th quadrant, where

⇒ sec²x > 0

⇒ f’(x) > 0

Thus, condition for f(x) to be increasing

Hence, f(x) is increasing on interval (–π/2, π/2).

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