Home
Class 12
MATHS
If the function e^(-x) f(X) assumes its ...

If the function e^(-x) f(X) assumes its minimum in the interval [0,1] at `x = 1//4` which of the following is true ?

A

`f'(x)ltf(X),1//4ltxlt3//4`

B

`f'(x)gtf(X),0ltxlt1//4`

C

`f'(x)ltf(X),0ltxlt1//4`

D

`f'(x)ltf(X),3//4ltxlt1`

Text Solution

Verified by Experts

The correct Answer is:
3
Let `g(X)=e^(-x)f(x)`
As `g'(x)gt0 , g(x)` is increasing
So for `xlt1/4, g(X)ltg(1/4)=0 or f(x)-f(x)e^(-x)lt0`
or `f'(x)ltf(x)in (0,1//4)`
Promotional Banner

Topper's Solved these Questions

  • MONOTONICITY AND MAXIMA MINIMA OF FUNCTIONS

    CENGAGE ENGLISH|Exercise Linked comprehension type|50 Videos

  • MONOTONICITY AND MAXIMA MINIMA OF FUNCTIONS

    CENGAGE ENGLISH|Exercise Matrix Match Type|14 Videos

  • MONOTONICITY AND MAXIMA MINIMA OF FUNCTIONS

    CENGAGE ENGLISH|Exercise Single Correct Answer Type|13 Videos

  • METHODS OF DIFFERENTIATION

    CENGAGE ENGLISH|Exercise Single Correct Answer Type|46 Videos

  • MONOTONOCITY AND NAXINA-MINIMA OF FUNCTIONS

    CENGAGE ENGLISH|Exercise Comprehension Type|6 Videos

Similar Questions

Explore conceptually related problems

Let f:[0,1] rarr R be a function.such that f(0)=f(1)=0 and f''(x)+f(x) ge e^x for all x in [0,1] .If the fucntion f(x)e^(-x) assumes its minimum in the interval [0,1] at x=1/4 which of the following is true ?

The function f(x) = tan ^(-1)x -x decreases in the interval

The function f(x)=x^(1//x) is increasing in the interval

The function f(x) = x^(x) , x gt 0 , is increasing on the interval

The mean value of the function f(x)= 2/(e^x+1) in the interval [0,2] is

The function f(x) = 7 + x - e^(x) is strictly increasing in the interval

The function f(x)=(2x^2-1)/x^4, x gt 0 decreases in the interval

Let a function f(x) be definded by f(x) =(x-|x-1|)/(x) which of the following is not true ?

y = f(x) which has differential equation y(2xy + e^(x)) dx - e^(x) dy = 0 passing through the point (0,1). Then which of the following is/are true about the function?

Let g(x)=int_0^(e^x) (f\'(t)dt)/(1+t^2) . Which of the following is true?