Consider \( f(x)=e^{x} \sec x-\sqrt{2} \cos x+x, x \in\left[\frac{-...

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Consider \( f(x)=e^{x} \sec x-\sqrt{2} \cos x+x, x \in\left[\frac{-\pi}{3}, \frac{\pi}{3}\right] \)
\( \mathrm{P} \)
(a) minimum value of \( f(x) \) is \( \left(\sqrt{2} e^{\frac{-\pi}{4}}-1-\frac{\pi}{4}\right) \)
W.
(b) minimum value of \( f(x) \) is \( \left(2 e^{\frac{-\pi}{3}}-\frac{1}{\sqrt{2}}-\frac{\pi}{3}\right) \)
(c) \( f^{\prime}\left(\frac{\pi}{3}\right) \geq f^{\prime}(x) \forall x \in\left[\frac{-\pi}{3}, \frac{\pi}{3}\right] \)
(d) \( f^{\prime}\left(\frac{\pi}{3}\right) \leq f^{\prime}(x) \forall x \in\left[\frac{-\pi}{3}, \frac{\pi}{3}\right] \)
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