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If f(x+y) = f(x) + f(y) + |x|y+xy^(2),AA...

If `f(x+y) = f(x) + f(y) + |x|y+xy^(2),AA x, y in R and f'(0) = 0`, then

A

f need not be differentiable at every non-zero x

B

f is differentiable for all `x in R`

C

f is twice differentiable at x = 0

D

None of the above

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The correct Answer is:
B
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ARIHANT MATHS-CONTINUITY AND DIFFERENTIABILITY-Exercise (Single Option Correct Type Questions)
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  3. The total number of points of non-differentiability of f(x) = min[|sin...

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  4. The function f(x)=[x]^2-[x^2] is discontinuous at (where [gamma] is t...

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  5. The function f(x) = (x^(2) - 1)|x^(2)-6x + 5|+cos|x| is not differenti...

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  6. If f(x) = {{:((1)/(e^(1//x))",",x ne 0),(0",",x = 0):} then

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  7. Given f(x) = (e^(x)-cos 2x - x)/(x^(2)),"for x" in R-{0} g(x) = {{:(f(...

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  8. The function g(x) = {{:(x+b",",x lt 0),(cos x",",x ge 0):} cannot be m...

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  9. The graph of function f contains the point P(1, 2) and Q(s, r). The e...

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  10. Consider f(x)=[(2(sinx-sinx-sin^3x))+|sinx-sin^3 x|)/(2(sinx-sin^3 x)...

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  11. If f(x+y) = f(x) + f(y) + |x|y+xy^(2),AA x, y in R and f'(0) = 0, then

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  12. Let f(x) = max. {|x^2 - 2 |x||,|x|} and g(x) = min. {|x^2 - 2|x||, |x|...

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  13. Let g(x)=[(3x^2-4sqrtx+1, x<1),(ax+b, x>=1)) If g(x) is continuous and...

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  14. Let f(x) be continuous and differentiable function for all reals and f...

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  15. Let [x] be the greatest integer function f(x)=(sin(1/4(pi[x]))/([x])) ...

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  16. If f(x) = {{:(b([x]^(2)+[x])+1",","for",x ge -1),(sin(pi(x+a))",","for...

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  17. If both f(x) & g(x) are differentiable functions at x=x0then the fun...

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  18. Number of points of non-differentiability of the function g(x) = [x^2...

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  19. If f(x) = ({x}g(x))/({x}g(x)) is a periodic function with period (1)/(...

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  20. If f((x)/(y))=(f(x))/(f(y)) for all x, y in R, y ne 0 and f'(x) exists...

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