Question

Let f be a twice differentiable function such that f’’(x) = –f(x) and f’(x) = g(x). If h’(x) = [f(x)]2 + [g(x)]2h(1) = 8 and 

h(0) = 2, then h(2) is equal to

Solution

Correct option is

None of these

 

  

              

            

Thus h’(x) = k, a constant, for all x Ïµ R. Hence h(x) = kx + m, so that formh(0) = 2, we get m = 2 and from h(1) = 8, we get k = 6. Therefore, h(2) = 14.     

SIMILAR QUESTIONS

Q1

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

Q2

 

Let f (x) = [x] and

               

Q3

Let

         

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

Q4

Given f’(2) = 6 and f’(1) = 4.  

       

Q5

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

                     

Q6

The domain of the derivative of the function

           

Q7

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

Q8

  

If f is differentiable for all x then 

Q9

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

Q10

If y2 = P(x) is a polynomial of degree 3, then    

              is equal to