# 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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