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Unformatted text preview: area under the graph of f(x) is a constant, it’s enough to minimize the area under the graph of T c (x) , the tangent line at the point c . This area is that of a trapezoid and as such is given by the formula (b  a) (T c (a) + T c (b))/2 . Since the tangent is a staight line, this is further equal to (b  a) T c ((a + b)/2) . By the observation above, the term T c ((a + b)/2) is greater than f((a + b)/2) for all values of c not equal to (a+b)/2 . Therefore, the area is minimized when c = (a + b)/2 , that is, for the tangent line at the midpoint....
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 Spring '10
 AlbertoDelgado
 Calculus, Combinatorics, Derivative, Differential Calculus, Slope, Mathematical analysis

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