Problem for the year

Calculus Level 2

λ=(f(5102)f(2015)f(c))(f2(2015)+f2(5102)+f(2015)f(5102)f2(c))\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][0,)f:[2015,5102] \rightarrow [0,\infty)be any continuous and differentiable function. Find the value of λ\lambda, such that there exists some c[2015,5102]c\in [2015,5102] which satisfies the equation above.

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