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f:RrarrR,f(x)=x^(3)+x^(2)f'(1)+xf''(2)+f...

`f:RrarrR,f(x)=x^(3)+x^(2)f'(1)+xf''(2)+f'''(3)" for all "x in R.`
The value of f(1) is

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The correct Answer is:
4
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f:RrarrR,f(x)=x^(3)+x^(2)f'(1)+xf''(2)+f'''(3)" for all "x in R. The value of f'(1)+f''(2)+f'''(3) is

f:RrarrR,f(x)=x^(3)+x^(2)f'(1)+xf''(2)+f'''(3)" for all "x in R. f(x) is

Knowledge Check

  • If f : R to R is a function such that f(x) = x^3 + x^2 f'(1) + x f" (2) + f ' ' '(3) for all x in R, then f (2) -f (1) is

    A
    `f(0)`
    B
    `-f(0)`
    C
    `f'(0)`
    D
    `-f'(0)`

  • Let f:R rarr R 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
    D
    4

  • 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
    `-4`
    C
    `-2`
    D
    8

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