Normal line at a point on a cubic: Find the point on the curve where the normal line has a slope of -12.

Since the normal line is perpendicular to the tangent line at the given point, we can relate the slope of the normal line, , to the slope of the tangent line, : .

From the equation of the curve we can find the derivative, . At the derivative equals the slope of the desired tangent line:

, or

. Hence , or .

Since this point is on the curve, we can find the corresponding y-coordinate from the equation of the curve: .