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A function f:R->R satisfies the relation...

A function `f:R->R` satisfies the relation `f((x+y)/3)=1/3|f(x)+f(y)+f(0)|` for all `x,y in R.` If `f'(0)` exists, prove that `f'(x)` exists for all `x, in R.`

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A DAS GUPTA-Differentiation-Exercise
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  3. A function f:R->R satisfies the relation f((x+y)/3)=1/3|f(x)+f(y)+f(0)...

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  11. If x=cost , y=loget then at t=pi/2, (d^2y)/(dx^2)+((dy)/(dx))^2=

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  13. If xe^(xy)=y+sin^2x then at x=0 (dy)/dx=

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