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# (a) Use a graph to estimate the absolute maximum and minimum values of the function to two decimal places.(b) Use calculus to find the exact maximum and minimum values.$f(x) = x - 2\cos x$, $-2 \leqslant x \leqslant 0$

## (a) SEE GRAPH.The absolute minimum value of $f(x)$ is $\approx-2.26$.The absolute maximum value of $f(x)$ is $\approx-1.17$ ; (b) Absolute minimum value is $-\frac{\pi}{6}-\sqrt{3}\approx-2.2556495832$ which occurs at $x=-\frac{\pi}{6}$.Absolute maximum value is $-2-2 \cos (2)\approx-1.1677063269$ which occurs at $x=-2$.

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