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Let {f{{({x}+{y})}}}={f{{({x})}}}+{f{{({y})}}}+{2}{x}{y}-{1} f

Question

Let $f (x + y) = f (x) + f (y) + 2 x y - 1$ for all real $x a n d y$ and $f (x)$ be a differentiable function. If $f^{p r i m e} (0) = cos α,$ the prove that $f (x) > 0 \forall x \in R ˙$

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Let

f (x + y) = f (x) + f (y) + 2 x y - 1

for all real

x a n d y

and

f (x)

be a differentiable function. If

f^{p r i m e} (0) = cos α,

the prove that

f (x) > 0 \forall x \in R ˙

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Question Text

Let

f (x + y) = f (x) + f (y) + 2 x y - 1

for all real

x a n d y

and

f (x)

be a differentiable function. If

f^{p r i m e} (0) = cos α,

the prove that

f (x) > 0 \forall x \in R ˙

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