Question

Now if it is given that there exists a positive real δ, such that f (h) = h for 0 < h < δ then find f’(x) and hence f (x).

Solution

Correct option is

f’(x) = 1, f (x) = x

Given       f (h) = h

   

  

⇒      f ’ (x) = 1, integrating both sides we get,  

⇒       f (x) = x + c  

Where   f (0) = 0   ⇒      c = 0  

so,         f (x) = x

Thus     f’ (x) = 1   and    f (x) = x

SIMILAR QUESTIONS

Q1

Let [.] denotes the greatest integer function and f (x) = [tan2x], then:

Q2

Let f be a real function satisfying f (x + z) = f (xf (yf (zfor all real xyz . If f (2) = 4 and f’ (0) = 3. Then find f (0) and f’ (2).

Q3

Let h(x) = min.{xx2} for every real number of x. Then:

Q4

Let f : R → R be a function defined by f (x) =  max. {xx3}. The set of all points where (x) is not differentiable is:

Q5

Let f (x) = Ï•(x) + ψ(x) and Ï•(a), ψ’(a) are finite and definite. Then:

Q6

If f (x) = x + tan and g(x) is the inverse of f (x) then g’ (x) is equal to:

Q7

If f (x) is differentiable function and (f (x). g(x)) is differentiable at x = a, then

Q8

        

Determine the value of ‘a’ if possible, so that the function is continuous

Q9

 for all real x and y. If f ’ (0) exists and equals to –1and f (0) = 1, find f ’(x).

Q10

Let f  be an even function and f ’(0) exists, then find f’(0).