Home
Class 12
MATHS
If x = -1 and x = 2 are extreme points o...

If x = -1 and x = 2 are extreme points of f(x) = `alpha log|x| + beta x^2 + x`, then

A

`alpha =-6,beta=1/3`

B

`alpha =-6,beta=-1/2`

C

`alpha =2,beta=-1/2`

D

`alpha = 2,beta=1/2`

Text Solution

Verified by Experts

The correct Answer is:
C
`f(X)=(alpha)/(x)+2betax+1`
`rarr 2betax^(2)+x+alpha`=0 has roots -1 and 2
`rarr alpha=2,beta =-1/2`
Promotional Banner

Topper's Solved these Questions

  • MONOTONICITY AND MAXIMA MINIMA OF FUNCTIONS

    CENGAGE|Exercise JEE Advanced Previous Year|17 Videos

  • MONOTONICITY AND MAXIMA MINIMA OF FUNCTIONS

    CENGAGE|Exercise Exercise (Numerical)|20 Videos

  • METHODS OF DIFFERETIATION

    CENGAGE|Exercise Question Bank|13 Videos

  • MONOTONOCITY AND NAXINA-MINIMA OF FUNCTIONS

    CENGAGE|Exercise Comprehension Type|6 Videos

Similar Questions

Explore conceptually related problems

The function f (x) = log (x + sqrt(x^2 +1)) is

Find the absolute extreme for f(x) = 1 - 2x - x^(2) in (-4,1)

If alpha < beta < gamma and sin gamma cos alpha=1, where alpha,gamma in[pi,2 pi], then the least integral value of f(x) = | x - alpha| + | x - beta| + |x - gamma| is

If alpha and beta are the zeroes of the polynomial p(x) = 4x^2 + 3x +7 then 1/(alpha) + 1/(beta) is equal to ……..

If alpha and beta are the roots of x^(2) + x + 1 = 0, then alpha^(2020) + beta^(2020) is

If alpha and beta are the roots of the equation 3x^(2) - 5x + 2 = 0 , find the value of (i) (alpha)/(beta) + (beta)/(alpha) (ii) alpha-beta (iii) (alpha^(2))/(beta) + (beta^(2))/(alpha)

If a and b are the roots of the polynomial f(x)=x^(2)-2x+3 , find the polynomial whose roots are (alpha-1)/(alpha+1), (beta-1)/(beta+1)

If alpha and beta are the roots of the equation x^2 + 2x +8=0 then the value of (alpha)/(beta) + (beta)/(alpha) is ………………….. .

Discuss the continuity of f(x)=(log|x|)sgn(x^2-1),x!=0.