Home
Class 12
MATHS
Let g(x)=f(logx)+f(2-logx)a n df^(x)<0AA...

Let `g(x)=f(logx)+f(2-logx)a n df^(x)<0AAx in (0,3)dot` Then find the interval in which `g(x)` increases.

Text Solution

Verified by Experts

The correct Answer is:
(0,e)
`g(x) =f(logx)+f(2-logx)`
`therefore g'(x) =[f(logx)-f'(2-logx)//x]`
g(x) increases if `g(x)gt0` Now `x gt0`
or `f(logx)-f(2-logx)gt0`
or `f(log x) gt f'(2-logx)`
or `log xlt2-logx[f''(x)lt0f,(x)]` is decreasing ]
or `log xlt 1`
or `0ltxlte`
Promotional Banner

Topper's Solved these Questions

  • MONOTONICITY AND MAXIMA MINIMA OF FUNCTIONS

    CENGAGE|Exercise Exercise 6.2|10 Videos

  • MONOTONICITY AND MAXIMA MINIMA OF FUNCTIONS

    CENGAGE|Exercise Exercise 6.3|6 Videos

  • MONOTONICITY AND MAXIMA MINIMA OF FUNCTIONS

    CENGAGE|Exercise Illustration|2 Videos

  • METHODS OF DIFFERETIATION

    CENGAGE|Exercise Question Bank|29 Videos

  • MONOTONOCITY AND NAXINA-MINIMA OF FUNCTIONS

    CENGAGE|Exercise Comprehension Type|6 Videos

Similar Questions

Explore conceptually related problems

Let g(x)=2f(x/2)+f(2-x) and f''(x)<0 , AA x in (0,2) .Then g(x) increasing in

e^(x+2logx)

If f(x)=(log)_x(logx) , then f'(x) at x=e is equal to......

int[f(logx)+f'(logx)]dx=

int[f(logx)+f'(logx)]dx=

y=x^(logx)+(logx)^(x)

∫ (1)/(x.logx.(2+logx))

If f(x)=log(logx)," then "f'(e)=