Home
Class 12
MATHS
If x =-1 and x=2 ar extreme points of f(...

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

A

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

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
Here, x=-1 and x=2 are extreme points of `f(x)= alpha log |x|+ beta x^(2)+x_(1)`, then
`f(x)=(alpha)/(x)+2 beta x+1`
`f'(-1)=-alpha-2 beta+1=0 " "...(i)`
[ at extreme point, `f'(x)=0`]
`f(x)=(alpha)/(2)+4beta+1=0" "..(i)`
On solving Eqs. (i) and (ii), we ge
`alpha2, beta=-(1)/(2)`
Promotional Banner

Similar Questions

Explore conceptually related problems

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

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

Find the extrema of f(x) = log (1 + x)- (x)/(1 + x), x gt -1

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

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

Let f:R rarr R, f(x)=x+log_(e)(1+x^(2)) . Then

Discuss the monotonicity and local extrema of the function f(x)=log (1+x)-(x)/(1+x), x gt -1 and hence find the domain where, log (1+x) gt (x)/(1+x)

Determine the point of maxima and minima of the function f(x)=1/8(log)_e x-b x+x^2,x >0, where bgeq0 is constant.

The domain of definition of f(x) = (log_2(x+2))/(x^2+3x+2)

Column I Column II f(x)=x^2logx f(x) has one point of minima f(x)=x(log)_e x q. f(x) has one point of maxima f(x)=(logx)/x r. f(x) increase x in (0,e) f(x)=x^(-x) s. f(x) decrease x in (0,1/e)