Not simultaneously even & odd function.

Calculus Level 4

f(x+y2n+1)=f(x)+f(y)2n+1 and nNf(x+y^{2n+1})=f(x)+f(y)^{2n+1} \ \text{and} \ n \in \mathbb{N}

Let f(x)f(x) be a real function not identically zero satisfying the above condition for any real numbers x,yx,y. And provided with f(0)0f'(0) \geq 0. Then find the value of f(10)f'(10).

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