Let c E R. Let g be a function with domain R. We know the following: g(0) = 0 • g is differentiable at 0 and g (0) = c %3D • for every x, y ER, g(x+y) = g(x) +2xy+ g(y). Prove that g is differentiable everywhere and find a formula for g'.
Let c E R. Let g be a function with domain R. We know the following: g(0) = 0 • g is differentiable at 0 and g (0) = c %3D • for every x, y ER, g(x+y) = g(x) +2xy+ g(y). Prove that g is differentiable everywhere and find a formula for g'.
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Transcribed Image Text:Let c E R. Let g be a function with domain R. We know the following:
• g(0) = 0
%3D
• g is differentiable at 0 and g'(0) = c
%3D
• for every x, y ER, g(x +y) = g(x) + 2xy+g(y).
Prove that g is differentiable everywhere and find a formula for g'.
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