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Problem 56

$53-56$ (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. $$f(x)=x-2 \cos x, \quad-2 \leqslant x \leqslant 0$$

Answer

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 $-\frac{\pi}{6}-\sqrt{3}[\approx-2.2557]$ which occurs at $x=-\frac{\pi}{6}$ Absolute maximum value is $-2-2 \cos (2)[\approx-1.1677]$ which occurs at $x=-2$

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