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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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Knowledge Check

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

    A
    30
    B
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    `-2`
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    8
  • Let f : RtoR be a function such that f(x)=x^3+x^2f'(1)+xf''(2)+f'''(3),x in R . Then f(2) equals

    A
    8
    B
    -2
    C
    -4
    D
    30
  • Let f:RtoR be a function such that f(x)=x^(3)+x^(2)f'(1)+xf''(2)+f'''(3) for x in R What is f(1) equal to :

    A
    `-2`
    B
    `-1`
    C
    0
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