For x ∈ [ 0 , π ] , let f ( x ) = 2 1 + ∫ 0 x ( t − x ) sin t d t . If M , m are its maximum and minimum, find M − m .

Leibniz differentiation gives f ( x ) = cos x − 1 ≤ 0 . Thus M = f ( 0 ) = 1/2 and m = f ( π ) = 1/2 − π , so M − m = π .

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MathematicsApplication of DerivativeMaxima-MinimaMedium2 minQB

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For $x \in [0, π]$ , let $f (x) = \frac{1}{2} + \int_{0}^{x} (t - x) sin t d t$ . If $M, m$ are its maximum and minimum, find $M - m$ .

Answer:

Solution:

Leibniz differentiation gives $f (x) = cos x - 1 \leq 0$ . Thus $M = f (0) = 1/2$ and $m = f (π) = 1/2 - π$ , so $M - m = π$ .

Stream:JEESubject:MathematicsTopic:Application of DerivativeSubtopic:Maxima-Minima

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