Question

Let f(x + y) = f(xf(y) for all xy Ïµ R and suppose that is differentiable at 0 and f’(0) = 4. If f(x0) = 8 then f’(x0) is equal to

Solution

Correct option is

32

Let y = 0. Then (x) = (xf (0), i.e., (x) [(0) – 1] = 0. So (x) = 0 or f(0) = 1. If (x) = 0 for all x, the f is clearly differentiable. Suppose therefore, that f is a non-zero function, so that (0) = 1. Since f is differentiable at x = 0, we have

           

Let x0 Ïµ R. Then

                  

           

SIMILAR QUESTIONS

Q1

 and n are integers, m ≠ 0, n > 0, and let p be the left hand derivative of |x – 1| at x = 1. If 

Q2

If f (x) = |x – 2| and g(x) = f (f (x)), then for x > 20, g’(x) is equal to

Q3

If f (9) = 9 and f’(9) = 4, then 

Q4

The derivatives of sec –1 [1/(2x2 – 1)] with respect to  at x = ½, is

Q5

Let F(x) = f(xg(xh(x) for all real x, where f(x), g(x) and h(x) are differentiable functions. At some point x0,  

                 

                   

Q6

If the function  then the value ofg’(1) is

Q8
Q9

The function y = (x2 + 1)50 is differentiated 70 times to get y70(x). Theny70(x) is a polynomial of degree is equal to

Q10

A function f (x) is defined for x > 0 and satisfies f(x2) = x3 for all x > 0. Then the value of f’(4) is