# Thread: Finding an equation to a line

1. ## Finding an equation to a line

I have this homework question, and I don't quite understand it. Can you please help me ?1. Find an equation of a line(s) that is tangent to the curve f(x)=2cos3x and whose slope is a minimum on the interval (0.2(pie))

2. ## Re: 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.