Given data:
The given expression for the function is f(x)=-2sin(x)cos(x).
Th egiven expression can be written as,
f(x)=-sin2x.
Differentiate the given function with respect to x an equate to zero.
[tex]\begin{gathered} f^{\prime}(x)=0 \\ \frac{d}{dx}(-\sin 2x)=0 \\ -2\cos 2x=0 \\ \cos 2x=0 \\ 2x=\frac{\pi}{2},\text{ }\frac{3\pi}{2} \\ x=\frac{\pi}{4},\text{ }\frac{3\pi}{4} \end{gathered}[/tex]Avoid x=π/4.
The value of function at x=π/3.
f(π/3)=-sin(2π/3)
=-0.866.
The value of at x=3π/4.
f(3π/4)=-sin(6π/4)
=-1
The value of function at x=π is,
f(π)=-sin(2π)
=0
Thus, the maximum value of function is 0 at x=π, and minimum value is -1 at x=3π/4.