Home
Class 12
MATHS
Let f(x)=x^(n) , n being a non-negative ...

Let `f(x)=x^(n)` , n being a non-negative integer, The value of `n` for which the equality `f'(x+y)=f'(x)+f'(y)` is valid for all `x,ygt0,` is

A

0,1

B

1,2

C

2,4

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
B
Promotional Banner

Similar Questions

Explore conceptually related problems

Let f(x)=x^n n being a non negative integer. The value of n for which the equality f'(a+b)=f'(a)+f'(b) is valid for all a.bgt0 is

Let f:R->R be a function such that f(x+y)=f(x)+f(y),AA x, y in R.

Let f(x)be a monotic ploynomial of degree (2m-1) where m in N Then the equation f(x)+f(3x)+f(5x)+….+f((2m -1) has

Let f(x) and g(x) be functions which take integers as arguments. Let f(x + y) =f(x)+ g(y) + 8 for all intege x and y. Let f(x) = x for all negative integers x and let g (8) = 17 . Find f(0).

Let f be differentiable function satisfying f((x)/(y))=f(x) - f(y)"for all" x, y gt 0 . If f'(1) = 1, then f(x) is

f(x)= 2x^(n) + a . If f(2)= 26 and f(4)= 138 then the value of f(3) is……..

Let f(x) be a real valued function such that f(0)=1/2 and f(x+y)=f(x)f(a-y)+f(y)f(a-x), forall x,y in R , then for some real a, (a)f(x) is a periodic function (b)f(x) is a constant function (c) f(x)=1/2 (d) f(x)=(cosx)/2

Let f(x) be periodic and k be a positive real number such that f(x + k) + f (x) = 0 for all x in R . Then the period of f(x) is

Let f(x)=(alphax)/(x+1),x ne -1 . Then, for what values of alpha is f[f(x)]=x?

Let f be a function satisfying f(x+y)=f(x) + f(y) for all x,y in R . If f (1)= k then f(n), n in N is equal to