Question

If f : R  R is a function such that (x) = x3 + x2 f’(1) + xf’’(2) + f’’’(3) for x Ïµ R then the value of f (2) is

Solution

Correct option is

–2

Putting x = 0 in the given equation, 

We have f (0) = f’’’ (3) and putting x = 1, we get f (1) = 1 + f’ (1) + f’’ (2) + f’’’ (3). Thus f (1) = (0) = 1 + f’ (1) + f’’ (2). Also differentiating the given equation, we have

         

          

Thus f’’’ (3) = 6 and f’’ (2) = 12 + 2 f’(1). Putting x = 1 in (i), we have  

         

                    

  

            

                      = 8 + 4(–5) + 2(2) + 6

                      = –2.

SIMILAR QUESTIONS

Q1

 is equal to

Q2

Which of the following could be not true if 

Q3

Suppose that f(x) = [x], the least integer function then

Q4

  is equal to

Q6
Q7
Q9

 for real and y. If f’(0) exists and equals – 1 and (0) = 1 then the value of f(2) is

Q10

 and n are integers, m ≠ 0, n > 0, and let p be the left hand derivative of |x – 1| at x = 1. If