Solveeit Logo

Question

Question: If the function f(x) = 2 tan x + (2a +1) log<sub>e</sub> \|secx \| + (a –2) x is increasing on R, th...

If the function f(x) = 2 tan x + (2a +1) loge |secx | + (a –2) x is increasing on R, then-

A

a Î (1/2, ¥)

B

a Î (–1/2, 1/2)

C

a = ½

D

a Î R

Answer

a = ½

Explanation

Solution

St. increasing ̃ f ¢ (x) ³ 0

̃ 2 sec2 x + (2a +1) tan x + (a –2) ³ 0

̃ 2 tan2 x + (2a +1) tan x + a ³ 0̃ (2a +1)2 –8a £ 0

̃ (2a –1)2 £ 0 ̃ 2a –1 = 0 ̃ a = ½