Let f(x) be a polynomial of degree 3 suc...

Let `f(x)` be a polynomial of degree 3 such that `f(3)=1,f^(prime)(3)=-1,f^('')(3)=0,a n df^(''')(3)=12.` Then the value of `f^(prime)(1)` is
(a)`12 ` (b)` 23 ` (c) `-13 ` (d) none of these

A

12

B

23

C

-13

D

none of these

Text Solution

Verified by Experts

`Let f(x)=a(x-3)^(3)+b(x-3)^(2)+c(x-3)+d`
`f(3)=1rArrd=1`
`f'(3)=-1rArrc=-1`
`f''(3)=0rArrb=0`
`f'''(3)=12rArra=2`
`therefore" "f'(x)=3a(x-3)^(2)+2b(x-3)+c`
`=6(x-3)^(2)-1`
`"or "f'(1)=23`

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