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Let f be function satisfying f(x+y)=f(x)...

Let f be function satisfying `f(x+y)=f(x)+f(y)` and `f(x)=x^(2)g(x)`, for all x and y, where `g(x)` is a continuous function. Then `f'(x)` is :

A

`g'(x)`

B

`g(0)`

C

`g(0)=g'(0)`

D

0

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The correct Answer is:
B
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MODERN PUBLICATION-DIFFERENTIABILITY AND DIFFERENTIATION -MCQs (LEVEL-II)
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  11. If y=(sinx)^cosx, then find (dy)/(dx).

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  13. If y=ce^(x//(x-a)), then 1/y(dy)/(dx) is equal to :

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  14. If y^2=P(x) is a polynomial of degree 3, then 2(d/(dx))(y^2dot(d^2y)/(...

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  15. If x=f(t) and y=g(t), then (d^2y)/(dx^2) is equal to

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  16. Derivative of (log x)^(4) is

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  17. If x=e^(y+e^(y+ . . . . .. "to "oo)),xgt0, then (dy)/(dx) is :

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  18. Suppose f(x) is differentiable at x=1 and lim(hto0)(1)/(h)(1+h)=5, the...

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  19. If f is a real valued differentiable function satisfying : |f(x)-f(y...

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  20. If f(x)=||x|-1|, then it is non - derivable at :

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