A function f is defined by f(x)=|x|^m|x-...

A function `f` is defined by `f(x)=|x|^m|x-1|^nAAx in Rdot` The local maximum value of the function is `(m ,n in N),` `1` (b) `m^nn^m` `(m^m n^n)/((m+n)^(m+n))` (d) `((m n)^(m n))/((m+n)^(m+n))`

`m^(n).n^(m)`

`(m^(m).n^(n))/(m+n)^(m+n)`

`(mn)^(mn)/(m+n)^(m+n)`

Text Solution

Verified by Experts

The correct Answer is:

Topper's Solved these Questions

MONOTONICITY MAXIMA AND MINIMA
ARIHANT MATHS ENGLISH|Exercise Exercise (More Than One Correct Option Type Questions)|16 Videos
MONOTONICITY MAXIMA AND MINIMA
ARIHANT MATHS ENGLISH|Exercise Exercise (Statement I And Ii Type Questions)|8 Videos
MONOTONICITY MAXIMA AND MINIMA
ARIHANT MATHS ENGLISH|Exercise Exercise For Session 5|8 Videos
MATRICES
ARIHANT MATHS ENGLISH|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|49 Videos
PAIR OF STRAIGHT LINES
ARIHANT MATHS ENGLISH|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|2 Videos

Similar Questions

Explore conceptually related problems

A function f is defined by f(x)=|x|^m|x-1|^nAAx in Rdot The local maximum value of the function is (m ,n in N) (a) 1 (b) m^n.n^m (c) (m^m n^n)/((m+n)^(m+n)) (d) ((m n)^(m n))/((m+n)^(m+n))

Let m and n be positive integers and x,y gt 0 and x+y =k, where k is constant. Let f (x,y) = x ^(m)y ^(n), then: (a) f (x,y) is maximum when x= (mk)/(m+n) (b) f (x,y) is maximuim where x =y (c) maximum value of f (x,y) is (m^(n)n ^(m) k ^(m+n))/((m+n)^(m+n)) (d) maximum value of f (x,y) is (k ^(m+n) m ^(m)n ^(n))/((m+n)^(m+n))

The minimum value of the fuction f(x) given by f(x)=(x^m)/(m)+(x^(-n))/(n) " where " 1/m+1/n =1" and " m gt 1 is

Find the value of the products: (3m-2n)(2m-3n)a t\ m=1,\ n=-1

The value of (m+n)^2+(m-n)^2 is:

lim_(n to oo){(1^(m)+2^(m)+3^(m)+...+ n^(m))/(n^(m+1))} equals

Simplify : ((a^(m))/(a^(n)))^(m+n)((a^(n))/(a^(l)))^(n+l)((a^(l))/(a^(m)))^(l+m)

The area of the parallelogram formed by the lines y=m x ,y=x m+1,y=n x ,a n dy=n x+1 equals. (|m+n|)/((m-n)^2) (b) 2/(|m+n|) 1/((|m+n|)) (d) 1/((|m-n|))

2{(m-n)/(m+n)+1/3((m-n)/(m+n))^(3)+1/5((m-n)/(m+n))^(5) +..} is equals to

If m, n in N , then int_(0)^(pi//2)((sin^(m)x)^(1/n))/((sin^(m)x)^(1/n)+(cos^(m)x)^(1/n))dx is equal to

ARIHANT MATHS ENGLISH-MONOTONICITY MAXIMA AND MINIMA-Exercise (Single Option Correct Type Questions)

sinx+cosx=y^2-y+a has no value of x for any value of y if a belongs to...
Text Solution
|
f: R->R is defined by f(x)=(e^(x^2)-e^(-x^2))/(e^(x^2)+e^(-x^2)) is :
Text Solution
|
Suppose that f(x) is a quadratic expresson positive for all real xdot ...
Text Solution
|
Let f(x)=min{1,cos x,1-sinx}, -pi le x le pi, Then, f(x) is
Text Solution
|
f(x)={2-|x^2+5x+6|,x!=2a^2+1,x=-2T h e nt h er a ngeofa , so that f(x...
Text Solution
|
Maximum number of real solution for the equation ax^(n)+x^(2)+bx+c=0...
Text Solution
|
Maximum number area of rectangle whose two sides are x=x(0),x=pi-x(0...
Text Solution
|
f(x)=-1+kx+k neither touches nor intecepts the curve f(x)= Iog x, then...
Text Solution
|
f(x) is polynomial of degree 4 with real coefficients such that f(x)=0...
Text Solution
|
A curve whose concavity is directly proportional to the logarithm of i...
Text Solution
|
f(x) = 4 tan x-tan^(2)x+tan^(3)x,xnenpi+(pi)/(2)
Text Solution
|
f (x)= {{:(3+|x-k|"," , x le k),(a ^(2) -2 + ( sin (x -k))/((x-k))"," ...
Text Solution
|
Let f(x) be linear functions with the properties that f(1) le f(2), f(...
Text Solution
|
If P(x) is polynomial satisfying P(x^(2))=x^(2)P(x)andP(0)=-2, P'(3//2...
Text Solution
|
Find the vertex and length of latus rectum of the parabola x^(2)=-4(y-...
Text Solution
|
Let f(x)=x^(2)-2xandg(x)=f(f(x)-1)+f(5-f(x)), then
Text Solution
|
Let f:NrarrN in such that f(n+1)gtf(f(n)) for all n in N then
Text Solution
|
The equation |2ax-3|+|ax+1|+|5-ax|=(1)/(2) possesses
Text Solution
|
Let a(1),a(2),a(n) be sequence of real numbers with a(n+1)=a(n)+sqrt(1...
Text Solution
|
A function f is defined by f(x)=|x|^m|x-1|^nAAx in Rdot The local max...
Text Solution
|