Let f  Be An Even Function And f ’(0) Exists, Then Find f’(0).

Why Kaysons ?

Video lectures

Access over 500+ hours of video lectures 24*7, covering complete syllabus for JEE preparation.

Online Support

Practice over 30000+ questions starting from basic level to JEE advance level.

Live Doubt Clearing Session

Ask your doubts live everyday Join our live doubt clearing session conducted by our experts.

National Mock Tests

Give tests to analyze your progress and evaluate where you stand in terms of your JEE preparation.

Organized Learning

Proper planning to complete syllabus is the key to get a decent rank in JEE.

Test Series/Daily assignments

Give tests to analyze your progress and evaluate where you stand in terms of your JEE preparation.

SPEAK TO COUNSELLOR ? CLICK HERE

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