Home
Class 12
MATHS
Let f be a twice differentiable function...

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

A

1

B

2

C

3

D

more than 3

Text Solution

Verified by Experts

The correct Answer is:
C
`f''(x)gt0 rArr f'(x)` is an increasing function
`h'(x)=sin2x(f'(sin^(2)x)-f'(cos^(2)x))`
`f'(x)=0 rArr sin^(2)x=0 rArr x=0`
or `f'(sin^(2)x)=f'(cos^(2)x) rArr sin^(2)x=cos^(2)x rArr tan^(2)x=1 rArr x = pm(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

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

Let f(x) be a differentiable function such that f(x)=x^2 +int_0^x e^-t f(x-t) dt then int_0^1 f(x) dx=

If f:R->R is a twice differentiable function such that f''(x) > 0 for all x in R, and f(1/2)=1/2. f(1)=1, then

Let f:(0,oo)->R be a differentiable function such that f'(x)=2-f(x)/x for all x in (0,oo) and f(1)=1 , then

Let f be a differentiable function such that f(1) = 2 and f'(x) = f (x) for all x in R . If h(x)=f(f(x)), then h'(1) is equal to

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) be a twice-differentiable function and f''(0)=2. Then evaluate lim_(xto0) (2f(x)-3f(2x)+f(4x))/(x^(2)).

Let f(x) be a continuous and differentiable function such that f(x)=int_0^xsin(t^2-t+x)dt Then prove that f^('')(x)+f(x)=cosx^2+2xsinx^2

Let f: R->R be a twice differentiable function such that f(x+pi)=f(x) and f''(x)+f(x)geq0 for all x in Rdot Show that f(x)geq0 for all x in Rdot

Let f be a twice differentiable function such that f^(primeprime)=-f(x),a n df^(prime)(x)=g(x),h(x)=[f(x)]^2+[g(x)]^2dot Find h(10)ifh(5)=11