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Let f :R to R be a function such that ...

Let `f :R to R` be a function such that `f(x) = x^3 + x^2 f' (0) + xf'' (2) , x in R` Then f(1) equals:

A

30

B

`-2`

C

`-23`

D

`2`

Text Solution

Verified by Experts

The correct Answer is:
C
`F'' (2) = 6`
` f' = (x) = 3x^2 + 2 x f' (0) + f'(1)`
` f'(0) = f''(1)`
` f'' (x) = 6x + 2f' (0) rArr f'' (1) = 6+2 f'(0)`
`f'(0) = -6, f'' = -6`
`f(x) = x^3 - 6x^2 - 6x + 6`
` f(1) = -5`
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