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A polynomial function f(x) is such that ...

A polynomial function f(x) is such that f'(4)= f''(4)=0 and f(x) has minimum value 10 at x=4 .Then

A

`f''(x)=4+ (x-4)^4`

B

`f(x) = 10 + (x-4)^4`

C

`f(x)-(x-4)^4`

D

non of these

Text Solution

Verified by Experts

The correct Answer is:
B
we have
f(4)=0 and f" (4)=0
`therefore f(x) =(x-4)^n+ gamma " where " n gt 3 `
It is given that f(x) has minimum at x=4 .Therefore , n=4
So, f(x) `(x-4)^4+gamma`
Now `f(x) = 10 rArr = gamma`
Hence `f(x) = (x-4)^4 + 10`
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