The graph of y =  x^3 + 9x^2 - 16x + 1 has a slope of 5 at two points.  Find the coordinates of the points. 

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Patricia - You are certainly on the right track!  However, do not forget that the first derivative of a function is simply the "slope" of the original function. To find out when the original function will have a slope of 5, simply set the first derivative (which you have already determined) equal to 5 and solve for x.  You will get "two" solutions for x since you are solving a quadratic equation.  Once you find each x value, simply plug them back into the original cubic equation to find the matching y coordinate. Hope this helped