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

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

Download JEE Question paper & Solution Download JEE Important questions Download Complete syllabus of Maths, Physics, Chemistry

Question

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

2
5
6
–2

medium

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) = f (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.