The attached image has the first derivative of the complex curve at the top, it is the general equation for the slope of the curve at any given point.
This question is about finding the x-coordinates of all the horizontal tangents to a complex curve. My approach was to set the first derivative of the curve to zero and then solve for x to get an equation that would yield the possible choices.
The attached image has the first derivative of the complex curve at the top, it is the general equation for the slope of the curve at any given point. It is correct because it was successfully used to calculate the equation of the tangent line at a given point. The steps below show a solution for 'x' but I'm not sure how that helps to find an x-coordinate for a horizontal tangent.
Would this be a reasonable approach or may other approaches be better.
To Find: The x coordinate of all the horizontal tangents.
Step by step
Solved in 2 steps
