Check whether Lagrange's mean value theorem is valid for $f (x) = sin x$ in $[0, \frac{π}{2}]$ .

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Solution

$f (x) = sin x$ is continuous and differentiable for all values of $x ϵ R .$ So in particular $f (x) = sin x$ is continuous in $[0, \frac{π}{2}]$ and differentiable in $[0, \frac{π}{2}] .$
Thus Lagrange's theorem is applicable.

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