Find the values of x on the interval [−π, π] where the tangent line to the graph of y = sin(x) cos(x) is horizontal. (Enter your answers as a comma-separated list.)

Question

rogue · Answer

A trig identity is $$a \sin u \cos u = \frac {a}{2} \sin (2u)$$So you can write your equation as$$y = \sin(x) \cos(x) = \frac {1}{2} \sin (2x)$$Use the crain rule here$$y' = \frac {d}{dx} \frac {1}{2}\sin (2x) = \frac {1}{2} \cos (2x) \frac {d}{dx} 2x = \cos (2x)$$The curve will have horizontal tangents when y' = 0.$$y' = 0 = \cos (2x)$$On the interval [-pi, pi], solution to that is$$x = \pm \frac {\pi}{4}, \pm \frac {3 \pi}{4}$$

anonymous · Answer

there is too many lines in your answer i cant nderstand it

rogue · Answer

Too many lines... :/ What part don't you get?
Also, by 'crain rule' I meant chain rule.

anonymous · Answer

what is the answer, it looks like this frac//sin{}[2xs[frac {dx) d and a whole lot of weird lines

rogue · Answer

:o oh, I think it isn't loading properly for you. Try refreshing the page or giving it more time.
Answer is:
x = - pi/4, + pi/4, - 3pi/4, +3pi/4

rogue · Answer

Here is a picture of what I typed.

anonymous · Answer

ahhh gotcha, well you got it right, good job :)