# Finding an equation to a line

I presume you know that the slope of the tangent line to a curve, at a specific point, is the derivative of the function at that point. The derivative here is f'(x)= -6sin(3x). On the interval from 0 to $2\pi$, -sin(x) has minimum value of -1 at $x= \pi/6$ and $x= 5\pi/6$ so the minimum slope of a tangent line to this curve is -6 at $x= \pi/6$ and $x= 6\pi/6$. Use either one of those to find an equation of a tangent line.