Minimizing Area: Proof that k is Independent of f(x) in a Tangent Problem

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The discussion focuses on proving that the value of k, which minimizes the area bounded by a concave down curve y=f(x) and its tangent line between points A and B, is independent of the function f(x). Participants emphasize the importance of visualizing the problem through sketches to clarify the relationships between the curve, tangent, and bounding lines. There is a call for more specificity in the question to facilitate assistance. The conversation highlights the need for a structured approach to the proof rather than simply seeking a solution. Overall, the thread encourages deeper engagement with the problem to achieve understanding.
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the graph of y=f(x) is concaved down over the interval (A,B)
ie f''(x)<0 for A=<x=<B
the tangent of the curve at point P(k,f(k)) meets lines x=A and x=B at P and Q respectively.
the value of k is such that the area bounded by the curve, the tangent and lines x=A and x=B is minimized.
Prove that k is independent of f(x).

somebody helps thanks
 
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