Problem for the year

Calculus Level 3

\[\lambda=\left( \frac{f(5102)-f(2015)}{f'(c)} \right) \left( \frac{f^2(2015)+f^2(5102)+f(2015)f(5102)}{f^2(c)} \right)\]

Let \(f:[2015,5102] \rightarrow [0,\infty)\)be any continuous and differentiable function. Find the value of \(\lambda\), such that there exists some \(c\in [2015,5102]\) which satisfies the equation above.

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