1 files changed, 55 insertions, 0 deletions
diff --git a/FSF-2020/approximations-and-optimizations/Critical Points/theorem.py b/FSF-2020/approximations-and-optimizations/Critical Points/theorem.py
new file mode 100644
index 0000000..7c82aa9
--- /dev/null
+++ b/FSF-2020/approximations-and-optimizations/Critical Points/theorem.py
@@ -0,0 +1,55 @@
+from manimlib.imports import*  
+
+class TheoremAnimation(ThreeDScene):
+    def construct(self):
+
+        axes = ThreeDAxes()
+
+        #----parabola: x**2+y**2
+        parabola1 = ParametricSurface(  
+            lambda u, v: np.array([
+                u,
+                v,
+                u**2+v**2
+            ]),v_min = -1, v_max = 1, u_min = -1, u_max = 1, checkerboard_colors = [TEAL_E],
+            resolution = (20, 20)).scale(1)     
+        
+        #----parabola: -x**2-y**2
+        parabola2 = ParametricSurface(
+            lambda u, v: np.array([
+                u,
+                v,
+                -u**2-v**2
+            ]),v_min = -1, v_max = 1, u_min = -1, u_max = 1, checkerboard_colors = [PURPLE_E,PURPLE_E],
+            resolution = (20, 20)).scale(1)
+               
+        self.set_camera_orientation(phi = 75 * DEGREES)  
+        self.begin_ambient_camera_rotation(rate = 0.4)  
+
+        d = Dot(np.array([0,0,0]), color = '#800000')           #---- critical point     
+        r = Rectangle(fill_color = '#C0C0C0',fill_opacity = 0.3).move_to(ORIGIN)    #----tangent plane         
+
+        parabola1_text = TextMobject("Maximum with horizontal tangent plane").scale(0.7).to_corner(UL)    
+     
+        parabola2_text = TextMobject("Minimum with horizontal tangent plane").scale(0.7).to_corner(UL)        
+
+        self.add(axes)
+        self.add_fixed_in_frame_mobjects(parabola2_text)
+        self.wait(1) 
+        self.play(Write(parabola1))
+        self.wait(1)
+        self.play(ShowCreation(d))
+        self.wait(1)
+        self.play(ShowCreation(r))     
+        self.wait(2)
+        self.play(FadeOut(parabola2_text),FadeOut(parabola1),FadeOut(r),FadeOut(d))  
+        
+        self.wait(1)
+        self.add_fixed_in_frame_mobjects(parabola1_text)
+        self.wait(1)
+        self.play(Write(parabola2))
+        self.wait(1)
+        self.play(ShowCreation(d))
+        self.wait(1)
+        self.play(ShowCreation(r))     
+        self.wait(2)