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Let f : R rarr R be a differentiable fun...

Let `f : R rarr R` be a differentiable function satisfying `f(x+y)=f(x) + f(y) +x^2y+xy^2` for all real number x and y . If `lim_(x rarr 0)(f(x))/x = 1`, then
The value of `f'(3)` is

A

8

B

10

C

12

D

18

Text Solution

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The correct Answer is:
B
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Knowledge Check

  • Let f : R rarr R be a differentiable function satisfying f(x+y)=f(x) + f(y) +x^2y+xy^2 for all real number x and y . If lim_(x rarr 0)(f(x))/x = 1 , then The value of f(9) is

    A
    240
    B
    356
    C
    252
    D
    730

  • f: R^(+) rarr R is continuous function satisfying f(x/y)=f(x) - f (y) AA x, y in R^(+) . If f'(1) = 1, then

    A
    f is unbounded
    B
    `lim_(x rarr0)f(1/x)=0`
    C
    `lim_(xrarr0)(f(1+x))/x=1`
    D
    `lim_(x rarr0)x.f(x)=0`

  • The number of linear functions of f satisfying f(x+f(x))=x+f(x) for all x in R is

    A
    0
    B
    1
    C
    2
    D
    4

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