Answer:
\(x=\dfrac{\pi}{4},-\dfrac{\pi}{4},\dfrac{3\pi}{4},-\dfrac{\pi}{4}\)
Step-by-step explanation:
Function: y= sin(x) cos(x)
To find the value of x where tangent line is horizontal on the interval [−π, π]
Slope = y'
\(y=\sin x\cos x\)
derivative of y
\(y'=\cos^2x-\sin^2x\)
For horizontal tangent line, slope must be 0
\(\cos^2x-\sin^2x=0\)
\(\tan^2x=1\)
\(\tan x=\pm 1\)
\(x=\dfrac{\pi}{4},-\dfrac{\pi}{4},\dfrac{3\pi}{4},-\dfrac{\pi}{4}\)
Horizontal tangents are,
\(y=\dfrac{1}{2}\ and \ y=-\dfrac{1}{2}\)
