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Math Help - Finding an equation to a line

  1. #1
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    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))
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  2. #2
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    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.
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