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## Homework Statement

Find the maximum value and minimum value of the function [tex] f(x) = cos 2x + 2sinx[/tex]

[tex] 0 \leq x \leq \frac{3\pi}{4}[/tex]

## Homework Equations

[tex] f(x) = cos 2x + 2sinx[/tex]

## The Attempt at a Solution

[tex] f(x) = cos 2x + 2sinx[/tex]

[tex] f'(x) = -2sin2x + 2cosx[/tex]

[tex] 0=-2sin2x + 2 cosx[/tex]

[tex] 2sin2x=2cosx[/tex]

[tex] sin2x = cosx[/tex]

[tex] 2sinxcosx = cosx[/tex]

[tex] 2sinx = 1 [/tex]

[tex] sin x = \frac{1}{2}[/tex]

[tex] x = \frac{\pi}{6}[/tex]

[tex] f''(x) = -4cos2x - 2sinx [/tex]

If I check, it is a max. But everything(in the domain) I check is max. What's up with this? Is my derivative wrong?