(a) Verify Rolle's theorem for : $f(x) = e^x(\sin x - \cos x)$ in $\l…

Previous year question for Engineering Mathematics-I.

Question

(a) Verify Rolle's theorem for : $f(x) = e^x(\sin x - \cos x)$ in $\left[\frac{\pi}{4}, \frac{5\pi}{4}\right]$.

(b) Find the extreme values of the function $\cos x \cdot \cos y \cdot \cos z$, where $x + y + z = \pi$.

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