13 Q The function f(x) = 2tan3x-3tan2x+12tanx +3, ∈(0, π2) is, (A) increasing - Maths - Limits and Derivatives

Question

13 Q The function f(x) = 2tan3x-3tan2x+12tanx
+3, ∈ ( 0 ,   π 2 ) is,

(A) increasing (B) decreasing
(C) increasing in (0, π / 4 ) a n d   d e c r e a sin g
  i n ( π / 4 ,   π / 2 )
(D) none of these

Aarushi Mishra · Accepted Answer

fx=2tan3x+3tan2x+12 tan x+3f'x=6 tan2x sec2x+6 tan x sec2x+12 sec2x=6sec2xtan2x+tan x+2Note: 6sec2x>0 and tan x>0 in x∈0, π2, therefore f'x>0 Hence fx is increasing

13.Q. The function f(x) = 2tan3x-3tan2x+12tanx +3, ∈ ( 0 , π 2 ) is, (A) increasing (B) decreasing (C) increasing in (0, π / 4 ) a n d d e c r e a sin g i n ( π / 4 , π / 2 ) (D) none of these

13.Q. The function f(x) = 2tan³x-3tan²x+12tanx +3, $\in (0, \frac{π}{2})$ is,

(A) increasing (B) decreasing
(C) increasing in (0, $π / 4) a n d d e c r e a \sin g i n (π / 4, π / 2)$
(D) none of these