Home
Class 12
MATHS
Let f(x) be real valued differentiable f...

Let `f(x)` be real valued differentiable function not identically zero such that `f(x+y^(2n+1)=f(x)+{f(y)}^(2n+1),nin Nandx,y` are any real numbers and `f'(0)le0.` Find the values of `f(5) andf'(10)`

A

3, 2

B

0, 1

C

1, 5

D

5, 1

Text Solution

AI Generated Solution

Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • DIFFERENTIATION

    ARIHANT MATHS ENGLISH|Exercise Exercise (More Than One Correct Option Type Questions)|61 Videos
  • DIFFERENTIATION

    ARIHANT MATHS ENGLISH|Exercise Exercise (Statement I And Ii Type Questions)|10 Videos
  • DIFFERENTIATION

    ARIHANT MATHS ENGLISH|Exercise EXAMPLE|3 Videos
  • DIFFERENTIAL EQUATION

    ARIHANT MATHS ENGLISH|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|26 Videos
  • DY / DX AS A RATE MEASURER AND TANGENTS, NORMALS

    ARIHANT MATHS ENGLISH|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|7 Videos

Similar Questions

Explore conceptually related problems

Let f(x) be a real valued function not identically zero, which satisfied the following conditions I. f(x + y^(2n + 1)) = f(x) + (f(y))^(2n+1), n in N, x, y are any real numbers. II. f'(0) ge 0 The value of f'(10), is

Let f(x) be a real valued function not identically zero, which satisfied the following conditions I. f(x + y^(2n + 1)) = f(x) + (f(y))^(2n+1), n in N, x, y are any real numbers. II. f'(0) ge 0 The value of f(1), is

Let f(x) be a real valued function not identically zero, which satisfied the following conditions I. f(x + y^(2n + 1)) = f(x) + (f(y))^(2n+1), n in N, x, y are any real numbers. II. f'(0) ge 0 The value of f(x), is

Let f(x) be a real function not identically zero in Z, such that for all x,y in R f(x+y^(2n+1))=f(x)={f(y)^(2n+1)}, n in Z If f'(0) ge 0 , then f'(6) is equal to

If f is real-valued differentiable function such that f(x)f'(x)<0 for all real x, then

If f is real-valued differentiable function such that f(x)f'(x)<0 for all real x, then

Let f(x) be real valued and differentiable function on R such that f(x+y)=(f(x)+f(y))/(1-f(x)dotf(y)) f(0) is equals a. 1 b. 0 c. -1 d. none of these

Let f(x) is a differentiable function on x in R , such that f(x+y)=f(x)f(y) for all x, y in R where f(0) ne 0 . If f(5)=10, f'(0)=0 , then the value of f'(5) is equal to

If f is a real- valued differentiable function satisfying |f(x) - f(y)| le (x-y)^(2) ,x ,y , in R and f(0) =0 then f(1) equals

Let f: R rarr R be a differentiable function satisfying f(x+y)=f(x)+f(y)+x^(2)y+xy^(2) for all real numbers x and y. If lim_(xrarr0) (f(x))/(x)=1, then The value of f(9) is