The graph defined by the equation 25x² + 16y² + 200x - 160y + 400 = 0 has horizontal tangent lines at two specific points. To find these points, one must apply implicit differentiation to derive dy/dx and set it equal to zero. This process reveals the conditions under which the slope of the tangent line is zero, indicating horizontal tangents. The graph represents an ellipse, confirming the existence of two such points.
PREREQUISITESStudents studying calculus, particularly those focusing on implicit differentiation and the analysis of curves, as well as educators teaching these concepts.
The easiest thing to do is to use implicit differentiation to get dy/dx, then set it to zero. Since the graph is an ellipse, there should be two points where dy/dx = 0.htoor9 said:Homework Statement
Where does the graph of 25x^2 + 16y^2 + 200x - 160y + 400 = 0 have a horizontal tangent line.
Homework Equations
dy/dx dx/dy or something not sure.
The Attempt at a Solution
Well I know that a horizontal tangent line would mean the slope is zero...but what exactly do I do?