Show that the function f(x) = (x-a)^2 (x-b)^2 + x takes the value for some value of .

MATHEMATICS · Subjective · AP · Calculus AB · Limits and Continuity · Limits and Continuity

Problem

Show that the function f(x)=(x−a)2(x−b)2+xf(x) = (x-a)^2 (x-b)^2 + x takes the value a+b2\frac{a+b}{2} for some value of x∈[a,b]x \in [a, b].

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