Let f be a differentiable real valued function satisfying f(x+y) = f(x) + f(2y) + 6xy(x+2y) for all x, y - Maths - Continuity and Differentiability

Question

Let f be a differentiable real valued function satisfying f(x+y) =
f(x) + f(2y) + 6xy(x+2y) for all x, y in R Then prove that f''(0),
f''(1),f''(2), are in AP

Ayushi Chaurasiya · Accepted Answer

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Regards

Let f be a differentiable real valued function satisfying f(x+y) = f(x) + f(2y) + 6xy(x+2y) for all x, y in R. Then prove that f''(0), f''(1),f''(2),... are in AP.