Find the points on a horizontal line

1. Sep 19, 2010

ahazen

Question: Find all points on the graph of the function f(x) = 2 sin(x) + (sin(x))2 at which the tangent line is horizontal. Consider the domain x = [0,2π).

f'(x)=2cos x+2sinxcosx...i think

No idea where to go after this...

2. Sep 19, 2010

Office_Shredder

Staff Emeritus
Ok, if the tangent line is horizontal, what does f'(x) have to be?

3. Sep 19, 2010

ahazen

f'(x)=2cosx +2sinx*(sinx)d/dx
=2cosx +2sinx*cosx
=cos (2+2sinx)

4. Sep 19, 2010

MysticDude

Hi there, the first thing that I would do is to factor out the 2cos(x).

1. 2cosx(sinx + 1) = 0

Note that this has to be equal to zero because when a tangent line is horizontal it has to be zero.

So all you have to do is find when sinx = -1 OR cosx = 0 on [0,2π)
So x can either be (3π)/2 (that's when sin(x) = -1) or π/2 (that's when cos(x) = 0).

I double checked this with my graphing calculator and these points are also the relative maxima, where the tangent line is 0.

5. Sep 19, 2010

ahazen

Thank you so much:) I really appreciate it:)

6. Sep 19, 2010

MysticDude

And just to show it it visually so you can fully understand:[PLAIN]http://img818.imageshack.us/img818/2223/mathp.png [Broken]

Last edited by a moderator: May 4, 2017
7. Sep 19, 2010

ahazen

Oh, ok:) that makes sense:) Thank you:)