Question

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

Solution

Correct option is

f ’(0) = 0

Since f is an even function. 

So,    f (–x) = f (x)           for all x                 …(i)

Also, f’ (0) exists

So,    Rf’(0) = Lf’(0)

  

  

  

SIMILAR QUESTIONS

Q1

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).

Q2

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

Q3

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

Q4

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

Q5

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

Q6

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

Q7

        

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

Q8

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

Q9

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).

Q10

Let f (x) = xnn being non-negative integer. Then find the value of n for which the equality f’(a + b) = f ’(a) + f ’ (b) is valid for all, ab > 0