Question

  

If f is differentiable for all x then 

Solution

Correct option is

a = 3/4, b = 9/4

Since f is differentiable for all x, in particular it is continuous at 2. But (2) = 4a – 2b + 3 and  so 4a – 2b + 3 = 2a

i.e. 2a – 2b + 3 = 0                    …(i)

Also f’(2) = a and f’(2+)

       

          

Thus 4a – b = a ⇒ 3a = b               …(ii)

Solving (i) and (ii) a = 3/4 and b = 9/4.  

SIMILAR QUESTIONS

Q1

 

If f’ is differentiable function and f’’(x) is continuous at x = 0 and f’’(0) =a, the value of  

                  

Q2

Let [.] denote the greatest integer function and . Then

Q3

Let f (x + y) = (xf (y) for all x and y. If f (5) = 2 and f’(0) = 3, then f’(5) is equal to

Q4

 

Let f (x) = [x] and

               

Q5

Let

         

The values of the coefficient a and b for which the function is continuous and has a derivative at x0, are

Q6

Given f’(2) = 6 and f’(1) = 4.  

       

Q7

Let R âŸ¶ R be such that f(1) = 3 and f’(1) = 6. Then

                     

Q8

The domain of the derivative of the function

           

Q9

If (0) = 0, f’(0) = 2 then the derivative of  at x = 0 is 

Q10

Let f and g be differentiable function such that f’(x) = 2g(x) and g’(x) = –f(x), and let T(x) = (f (x))2 – (g(x))2. Then T’(x) is equal to