Home
Class 12
MATHS
f'(sin^(2)x)lt f'(cos^(2)x) for x in...

`f'(sin^(2)x)lt f'(cos^(2)x)` for `x in`

A

`(-(pi)/(4),(pi)/(4))`

B

`(-(pi)/(2),-(pi)/(4))uu(pi)/(4),(pi)/(2))`

C

`(-(pi)/(4),0)uu(pi)/(4),(pi)/(2))`

D

`(-(pi)/(2),(pi)/(2))`

Text Solution

Verified by Experts

The correct Answer is:
A
`f'(sin^(2)x)ltf'(cos^(2)x) rArr sin^(2)x lt cos^(2)x rArr tan^(2) x lt 1`
`rArr x in (-(pi)/(4),(pi)/(4))`
Promotional Banner

Topper's Solved these Questions

  • MONOTONOCITY AND NAXINA-MINIMA OF FUNCTIONS

    CENGAGE|Exercise Multiple Correct Answer Type|10 Videos

  • MONOTONICITY AND MAXIMA MINIMA OF FUNCTIONS

    CENGAGE|Exercise JEE Advanced Previous Year|17 Videos

  • PAIR OF STRAIGHT LINES

    CENGAGE|Exercise Exercise (Numerical)|5 Videos

Similar Questions

Explore conceptually related problems

Let f be a twice differentiable function such that f''(x)gt 0 AA x in R . Let h(x) is defined by h(x)=f(sin^(2)x)+f(cos^(2)x) where |x|lt (pi)/(2) . The number of critical points of h(x) are

Let f'(sin x) lt 0 and f''(sin x) gt 0 AA x in (0, pi/2) and g (x) = f (sin x) + f (cos x) , then

Let f(x)=|[1+sin ^2 x, cos ^2 x , 4 sin 2 x],[ sin ^2 x ,1+cos ^2 x , 4 sin 2 x],[ sin ^2 x , cos ^2 x , 1+4 sin 2 x]| , the maximum value of f(x) is

int(1-7cos^(2)x)/(sin^(7)xcos^(2)x)dx=(f(x))/((sinx)^(7))+C , then f(x) is equal to

Consider function f(x) = sin^(-1) (sin x) + cos^(-1) (cos x), x in [0, 2pi] (a) Draw the graph of y = f (x) (b) Find the range of f(x) (c) Find the area bounded by y = f(x) and x-axis

Find the range of f(x) = (sin^(-1) x)^(2) + 2pi cos^(-1) x + pi^(2)

Find f'(x)" if "f(x)= (sin x)^(sin x) for all 0 lt x lt pi .

"Let "f(x)=|{:(cos(x+x^(2)),sin (x+x^(2)),-cos(x+x^(2))),(sin (x-x^(2)),cos (x-x^(2)),sin (x-x^(2))),(sin 2x, 0, sin (2x^(2))):}|. Find the value of f'(0).

If f(x) = |{:( cos (2x) ,, cos ( 2x ) ,, sin ( 2x) ), ( - cos x,, cosx ,, - sin x ), ( sinx,, sin x,, cos x ):}| , then

Let f(x) = |(2cos^2x, sin2x, -sinx), (sin2x, 2 sin^2x, cosx), (sinx, -cosx,0)| , then the value of int_0^(pi//2){f(x) + f'(x)} dx is