Question:

Rolle's Theorem and Mean Value theorem ?

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Taking function f(x)= xsin(x) + cos(x)+ cos²x,show that π/2 < f(x) < 2

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  1. This is not true.  Notice that f(0) = 2 and f(pi/2) = pi/2.  Thus, there is no hope to prove that pi/2 &lt; f(x) &lt; 2.

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