# Find the absolute maximum, M, and minimum, m, of f(x)=cosx-sin^{2x} on the domain \left [...

## Question:

Find the absolute maximum, M, and minimum, m, of {eq}f(x)=cosx-sin^{2} x {/eq} on the domain {eq}\left [ \pi,2\pi \right ] {/eq}.

## Absolute maximum and absolute minimum

The value where the most increased function is known as absolute maximum and the value where the most decreased function is known as the absolute minimum of the function.

We have the function

{eq}f(x)= \cos (x) - \sin^{2}(x) \\ {/eq}

Differentiating the function

{eq}f'(x)=-\sin \left( x \right) \left( 2\,\cos...

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