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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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  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|} th...

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  13. If x dy = y (dx + y dy), y > 0 and y (1) = 1, then y (−3) is equal t...

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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 gt -1),(sin(pi(x + a))",","f...

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  17. If f(x) and g(x) are non-periodic functions, then h(x)=f(g(x)) is

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

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  19. Find dy/dx if y= xtanx

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

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