Let f(x) be a continuous function, whose first and second derivatives are continuous on [0,2pi] and f''(x) >= 0 for all x in [0,2pi]. Show that

\[ \int_0^{2 \pi } f(x) \cos x \, dx \geq 0 \]

Let f(x) be a continuous function, whose first and second derivatives are continuous on [0,2pi] and f''(x) >= 0 for all x in [0,2pi]. Show that

\[ \int_0^{2 \pi } f(x) \cos x \, dx \geq 0 \]

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