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

# If f : R → R is A Function Such That f (x) = x3 + x2 f’(1) + xf’’(2) + f’’’(3) For x Ïµ R then The Value Of f (2) Is

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## Question

### 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

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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