(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Find all points on the graph of the function

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

at which the tangent line is horizontal.

2. Relevant equations

- Power rule

- Chain rule

- Product rule?

3. The attempt at a solution

So I want all points at which the tangent line to this function has a slope of zero.

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

[tex]f'(x)=2cosx+(sinx)^2[/tex]

[tex]f'(x)=2cosx+2sinx*\frac{d}{dx}sinx[/tex]

[tex]f'(x)=2cosx+2sinx*cosx[/tex]

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

...?

How do I go from here? I know to set that last equation equal to zero and find all the solutions, but just how do I find those solutions?

The solution from the book says:

[tex](\frac{\pi}{2}+2n\pi,3),(\frac{3\pi}{2}+2n\pi,-1)[/tex] where n an integer

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# Homework Help: Find all points on graph of f(x)=2sinx+sin^2x where slope = 0

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