Rename FSF-2020/approximations-and-optimizations/Critical-Points/file3_Tangent_plane_at_extrema_of_a_function.py to FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Critical-Points/file3_Tangent_plane_at_extrema_of_a_function.py

1 files changed, 73 insertions, 0 deletions

diff --git a/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Critical-Points/file3_Tangent_plane_at_extrema_of_a_function.py b/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Critical-Points/file3_Tangent_plane_at_extrema_of_a_function.py
new file mode 100644
index 0000000..e674113
--- /dev/null
+++ b/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Critical-Points/file3_Tangent_plane_at_extrema_of_a_function.py
@@ -0,0 +1,73 @@
+from manimlib.imports import*  
+
+#---- tangent plane to minima of the function
+class firstScene(ThreeDScene):
+    def construct(self):
+
+        axes = ThreeDAxes()
+        label_x = TextMobject("$x$").shift([5.5,-0.5,0]) #---- x axis
+        label_y = TextMobject("$y$").shift([-0.5,5.5,0]).rotate(-4.5) #---- y axis
+
+        #---- parabola: f(x,y) = x**2 + y**2
+        parabola = 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 = [GREEN_E,GREEN_D,GREEN_C,GREEN_B], resolution = (20, 20)).scale(1)     
+        
+        d = Dot(np.array([0,0,0]), color = '#800000') # ---- critical point     
+
+        tangent_plane = Rectangle(fill_color = '#C0C0C0', fill_opacity = 0.3).move_to(ORIGIN).fade(0.7)  # ----tangent plane         
+     
+        parabola_text = TextMobject("Minimum with horizontal tangent plane").scale(0.7).to_corner(UL)  
+
+        self.set_camera_orientation(phi = 75 * DEGREES, theta = 45 * DEGREES)  
+        self.begin_ambient_camera_rotation(rate = 0.2) 
+        self.add(axes)
+        self.add(label_x)
+        self.add(label_y)
+        self.add_fixed_in_frame_mobjects(parabola_text)
+        self.wait(1) 
+        self.play(Write(parabola))
+        self.play(ShowCreation(d))
+        self.wait(1)
+        self.play(ShowCreation(tangent_plane))     
+        self.wait(2)
+        self.play(FadeOut(parabola_text),FadeOut(parabola),FadeOut(tangent_plane),FadeOut(d),FadeOut(label_x),FadeOut(label_y),FadeOut(axes))  
+
+
+#---- tangent plane to maxima of the function
+class secondScene(ThreeDScene):
+    def construct(self):
+
+        axes = ThreeDAxes()
+        label_x = TextMobject("$x$").shift([5.5,-0.5,0]) #---- x axis
+        label_y = TextMobject("$y$").shift([-0.5,5.5,0]).rotate(-4.5) #---- y axis   
+        
+        #----parabola: g(x,y) = -x**2-y**2
+        parabola = 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 = [BLUE_E,BLUE_D,BLUE_C,BLUE_B], resolution = (20, 20)).scale(1)
+        
+        d = Dot(np.array([0,0,0]), color = '#800000') #---- critical point     
+
+        tangent_plane = Rectangle(fill_color = '#C0C0C0',fill_opacity = 0.3).move_to(ORIGIN).fade(0.7) #---- tangent plane         
+
+        parabola_text = TextMobject("Maximum with horizontal tangent plane").scale(0.7).to_corner(UL)        
+
+        self.set_camera_orientation(phi = 75 * DEGREES, theta = 45 * DEGREES)  
+        self.begin_ambient_camera_rotation(rate = 0.2) 
+        self.add(axes)
+        self.add(label_x)
+        self.add(label_y)
+        self.add_fixed_in_frame_mobjects(parabola_text)
+        self.wait(1) 
+        self.play(Write(parabola))
+        self.play(ShowCreation(d))
+        self.wait(1)
+        self.play(ShowCreation(tangent_plane))     
+        self.wait(2)