Home
Class 12
MATHS
Given f' (1) = 1 and d/(dx)f(2x)=f'(x) ...

Given `f' (1) = 1 and d/(dx)f(2x)=f'(x) AA x > 0`. If `f' (x)` is differentiable then there exists a number `c in (2,4)` such that `f'' (c)` equals

A

`-1//4`

B

`-1//8`

C

`1//4`

D

`1//8`

Text Solution

Verified by Experts

The correct Answer is:
B
Promotional Banner

Similar Questions

Explore conceptually related problems

If f(x) = 0 for x lt 0 and f(x) is differentiable at x = 0, then for x gt 0, f(x) may be

Let f : R rarr R satisfying |f(x)|le x^(2), AA x in R , then show that f(x) is differentiable at x = 0.

Let f(x) = ||x|-1|, then points where, f(x) is not differentiable is/are

Let f(x) be a differentiable function in the interval (0, 2) then the value of int_(0)^(2)f(x)dx

If f(x) = |1 -x|, then the points where sin^-1 (f |x|) is non-differentiable are

If (d)/(dx)f(x)=cos x +sin x and f(0)=2 , then f(x)=.....

If f(x) is continuous function in [0,2pi] and f(0)=f(2 pi ), then prove that there exists a point c in (0,pi) such that f(x)=f(x+pi).

Prove that the function f given by f(x)= |x-1|, x in R is not differentiable at x=1

A function f : R to R satisfies the equation f(x+y) = f (x) f(y), AA x, y in R and f (x) ne 0 for any x in R . Let the function be differentiable at x = 0 and f'(0) = 2. Show that f'(x) = 2 f(x), AA x in R. Hence, determine f(x)

Let f(x) be a fourth differentiable function such f(2x^2-1)=2xf(x)AA x in R, then f^(iv)(0) is equal