Home
Class 12
MATHS
If f is an odd continuous function in [-...

If `f` is an odd continuous function in `[-1,1]` and differentiable in `(-1,1)` then
a. `f'(A)=f(1)" for some "A in (-1,0)`
b. `f'(B) =f(1)" for some "B in (0,1)`
c. `n(f(A))^(n-1)f'(A)=(f(1))^(n)" for some " A in (-1, 0), n in N`
d. `n(f(B))^(n-1)f'(B)=(f(1))^(n)" for some" B in (0,1), n in N`

A

`f'(A)=f(1)" for some "A in (-1,0)`

B

`f'(B) =f(1)" for some "B in (0,1)`

C

`n(f(A))^(n-1)f'(A)=(f(1))^(n)" for some " A in (-1, 0), n in N`

D

`n(f(B))^(n-1)f'(B)=(f(1))^(n)" for some" B in (0,1), n in N`

Text Solution

Verified by Experts

The correct Answer is:
A, B, D
Promotional Banner

Topper's Solved these Questions

  • DY / DX AS A RATE MEASURER AND TANGENTS, NORMALS

    ARIHANT MATHS|Exercise Exercise (Statement I And Ii Type Questions)|7 Videos

  • DY / DX AS A RATE MEASURER AND TANGENTS, NORMALS

    ARIHANT MATHS|Exercise Exercise (Passage Based Questions)|8 Videos

  • DY / DX AS A RATE MEASURER AND TANGENTS, NORMALS

    ARIHANT MATHS|Exercise Exercise (Single Option Correct Type Questions)|33 Videos

  • DIFFERENTIATION

    ARIHANT MATHS|Exercise Exercise For Session 10|4 Videos

  • ELLIPSE

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|26 Videos

Similar Questions

Explore conceptually related problems

Suppose that f(x) is continuous in [0, 1] and f(0) = 0, f(1) = 0 . Prove f(c) = 1 - 2c^(2) for some c in (0, 1)

f_(n)(x)=e^(f_(n-1)(x))" for all "n in N and f_(0)(x)=x," then "(d)/(dx){f_(n)(x)} is

Let f be a differentiable function satisfying [f(x)]^(n)=f(nx)" for all "x inR. Then, f'(x)f(nx) a. f(x) b. 0 c. f(x)f'(nx) d. none of these

Let f(x) = int_(-2)^(x)|t + 1|dt , then a. f(x) is continuous in [-1, 1] b. f(x) is differentiable in [-1, 1] c. f'(x) is continuous in [-1, 1] d. f'(x) is differentiable in [-1, 1]

lf is a differentiable function satisfying f(1/n)=0,AA n>=1,n in I , then

Let f be a continuous function on R such that f (1/(4n))=sin e^n/(e^(n^2))+n^2/(n^2+1) Then the value of f(0) is

If f(x) =x^n and if f’ (1) = 10, find n.

If function f:AtoB is a bijective , then f^(-1)of is a. fof^(-1) b. f c. f^(-1) d. I_(A) (the identity map of the set A)

Let f : R rarr R be a differentiable function at x = 0 satisfying f(0) = 0 and f'(0) = 1, then the value of lim_(x to 0) (1)/(x) . sum_(n=1)^(oo)(-1)^(n).f((x)/(n)) , is a. 0 b. -log2 c. 1 d. e