Update app.py

app.py

@@ -840,6 +840,22 @@ make sure the question is CLEAR about what regions you intend to be included in
 14. In expanding or factoring polynomial expressions, be careful not to make errors
    - (1+u^2)^2 is equal to (1+2u^2+u^4), NOT equal to (1+3u^2+u^4) 
 
+15. When finding points where dy/dx = 0 in parametric equations:
+ - (a) First find the ratio dy/dx = (dy/dt)/(dx/dt)
+ - (b) Find t-values where this ratio equals 0
+ - (c) CRITICAL: For any t-values where both dy/dt = 0 AND dx/dt = 0:
+ - (d) These are potential "corner points" or cusps
+ - (e) Must apply parametric L'Hôpital's rule:
+     * Define f(t) = dy/dt and g(t) = dx/dt
+     * If f(t₀) = g(t₀) = 0, evaluate lim[t→t₀] f'(t)/g'(t)
+     * This limit, if it exists, gives the actual slope at t₀
+     Only conclude the tangent is horizontal if this limit equals 0
+ - (f) For each solution t:
+   - Calculate the corresponding point (x(t), y(t))
+   - Verify the point lies on the curve
+   - State whether it's a regular point or special point (cusp, corner, etc.)
+
+
 """
         
 #Consider