Let f(x) = lambda + mu|x|+nu|x|^2, where...

Let `f(x) = lambda + mu|x|+nu|x|^2`, where `lambda,mu, nu in R`, then `f'(0)` exists if

`mu =0`

v =0

` lambda=0`

`mu= v`

Text Solution

Verified by Experts

The correct Answer is:

Topper's Solved these Questions

CONTINUITY AND DIFFERENTIABILITY
AAKASH INSTITUTE|Exercise Section - C ( More than one options are correct )|5 Videos
CONTINUITY AND DIFFERENTIABILITY
AAKASH INSTITUTE|Exercise Section - D|6 Videos
CONTINUITY AND DIFFERENTIABILITY
AAKASH INSTITUTE|Exercise Assignment ( section -A)|61 Videos
CONIC SECTIONS
AAKASH INSTITUTE|Exercise SECTION - J ( Aakash Challengers Questions )|14 Videos
DETERMINANTS
AAKASH INSTITUTE|Exercise SECTION - J|12 Videos

Similar Questions

Explore conceptually related problems

Let f(x)=a+b|x|+c|x|^(2) , where a,b,c are real constants. The, f'(0) exists if

Verify that the function y = 2lambda x + (mu)/(x) where lambda, mu are arbitary constants is a solution of the differential equation x^(2)y'' + xy' - y = 0 .

Consider the system of linear equations x+y+z=5 , x+2y+lambda^(2)z=9,x+3y+lambda z=mu ,where lambda,mu in R .Then,which of the following statement is NOT correct?

If f(x)={:{([x]+[-x] , xne 0), ( lambda , x =0):} where [.] denotes the greatest function , then f(x) is continuous at x =0 , " for" lambda

Let f: R to R be defined as f(x)={{:(x^(5) sin""((1)/(x))+5x^(2)",",x lt0),(" 0,", x=0),(x^(5) cos""((1)/(x))+ lambdax^(2)",",x gt 0):} The value of lambda for which f''(0) exists , is ____________

Let I_(n)=int(x^(n))/(sqrt(x^(2)+2x+5))dx then I_(n)=(x^(m-1))/(n)sqrt(x^(2)+2x+5)-lambda I_(n-1)-mu I_(n-2) where lambda,mu and m' are involving n' then

For a,b,in R and a!=0, the equation ax^(2)+bx+c=0 and x^(2)+2x+3=0 have atleast one common root if (a)/(lambda)=(b)/(mu)=(c)/(Psi) where lambda,mu and Psi are positive integers.The least value of (lambda+mu+Psi) is

Let f(x)={(5^(1//x)"," , x lt 0),(lambda[x]",",x ge0):} and lambda in R , then at x = 0

If |{:(x+3,x+4,x+lambda),(x+4,x+5,x+mu),(x+5,x+6,x+v):}|=0 where lambda,mu,v are in A.P then prove that this is an identity in x.

AAKASH INSTITUTE-CONTINUITY AND DIFFERENTIABILITY-Section -B

lim(x->0)((4^x+9^x)/2)^(1/x)
Text Solution
|
If underset (xrarr0)"lim"(cos+asinbx)^(x/y)=e^(2) then the values of a...
Text Solution
|
lim(x to 0) (sqrt(1- cos 2x))/(sqrt2x) =
Text Solution
|
limx->(2^+) ([x]^3/3-[x/3]^3) is
Text Solution
|
The value of f(0) so that f(x) = ((4x^(x)-1)^(3))/(sin(x/4)log(1+(x^...
Text Solution
|
If f(x)= {:{((x^(2) + 3x+p)/(2(x^(2)-1)) , xne 1),(5/4, x = 1):} is co...
Text Solution
|
In order that the function f(x)=(x+1)^(cotx) is continuous at x = 0, f...
Text Solution
|
The number of points at which the function f(x) = 1/ (log |2x|) is di...
Text Solution
|
If f(x)={:{(xe^(-(1/(|x|) + 1/x)), x ne 0),(0 , x =0 ):} then f(x) is
Text Solution
|
The set of points where f(x)=x/(1+|x|) is differentiable is
Text Solution
|
The function |x^2 - 3x+2| + cos |x| is not differentiableat x=
Text Solution
|
At x = 0 , the function y = e^(-|x|) is
Text Solution
|
Let f(x) = lambda + mu|x|+nu|x|^2, where lambda,mu, nu in R, then f'(0...
Text Solution
|
If {x} denotes the fractional part of x, then underset(x to 0)(lim) ({...
Text Solution
|
Let f(x) = [x] , g(x)= |x| and f{g(x)} = h(x) ,where [.] is the gre...
Text Solution
|
A function f is defined by f(x^(2) ) = x^(3) AA x gt 0 then f(4) equ...
Text Solution
|
If 3sin(x y)+4cos(x y)=5,t h e n(dy)/(dx)= -y/x (b) (3sin(x y)+4c...
Text Solution
|
Let f(x) = max { 4, 1+x^(2) ,x^(2) -1} AA x in R Total numbner of poi...
Text Solution
|
Let g(x) be the inverse of the function f(x) ,and f'(x) 1/(1+ x^(3)) ...
Text Solution
|
If f is a real- valued differentiable function satisfying |f(x) - f(y)...
Text Solution
|