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Let f(X) be a polynomila of degree four ...

Let f(X) be a polynomila of degree four having extreme values at x =1 and x=2.If `lim_(xrarr0) [1+(f(x))/(x^(2))]=3` then f(2) is equal to

A

-8

B

-4

C

0

D

4

Text Solution

Verified by Experts

The correct Answer is:
3
`f(X)=0 at x=1 and x=2`
or f(1)=0 and f(2)=0
Also `underset(xrarr0)lim (f(x))/(x^(2))=2`
`therefore f(X)=ax^(4)+bx^(3)+2x^(3)`
`rarr f(X) =4ax^(3)+3bx^(2)+4x`
`therefore f(1)=4a+3b+4`
and f(2)=32a+12b+8
on solving 1 and 2 we get
`4a=2 rarr =1/2 therefore b=-2`
`therefore =(x^(4))/(2)-2x^(3)+2x^(3)`
Hence f(2)=8-16+8=0
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