Perpetually Bisected Tangent

Calculus Level 4

Let \(f(x)\) be a real-valued function in the first quadrant of the \(xy\) plane that passes through the point \((5, 10)\). If one draws a tangent line to any point \(P\) on \(f(x)\), then the portion of the tangent lying within the first quadrant is always bisected at \(P\).

Calculate \(f(25)\).

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