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

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) Examine the function $f = xy(a - x - y)$ for extreme values.

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