Question: (a) Use the Mean-Value Theorem to show that if \(f\) is differentiable on an open interval \(I\), and if \(\left|f^{\prime}(x)\right| \geq M\) for all values of \(x\) in \(I\), then

for all values of \(x\) and \(y\) in \(I\).

(b) Use the result in part (a) to show that

for all values of \(x\) and \(y\) in the interval \((-\pi / 2, \pi / 2)\)

(c) Use the result in part (b) to show that

for all values of \(x\) and \(y\) in the interval \((-\pi / 2, \pi / 2)\).

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