Update file1_Extrema_over_g(x,y)=k.py

1 files changed, 9 insertions, 6 deletions

diff --git a/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Lagrange-Multipliers/file1_Extrema_over_g(x,y)=k.py b/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Lagrange-Multipliers/file1_Extrema_over_g(x,y)=k.py
index 17f31ac..17ba858 100644
--- a/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Lagrange-Multipliers/file1_Extrema_over_g(x,y)=k.py
+++ b/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Lagrange-Multipliers/file1_Extrema_over_g(x,y)=k.py
@@ -1,14 +1,18 @@
 from manimlib.imports import*
+import math as m
 
 class firstScene(ThreeDScene):
     def construct(self):
-        axes = ThreeDAxes()
+        axes = ThreeDAxes().fade(0.4)        
+        label_x = TextMobject("$x$").shift([5.5,-0.5,0]).fade(0.4)  #---- x axis
+        label_y = TextMobject("$y$").shift([-0.5,5.5,0]).rotate(-4.5).fade(0.4)  #---- y axis
+
         surface = ParametricSurface(
             lambda u, v: np.array([
                 u,
                 v,
                 u**2+v**2+u**3-v**3
-            ]),u_min=-0.5,u_max=0.5, v_min=-0.5,v_max=0.5).scale(5).shift([0,1,2.5]).set_color('#F0FFFF').fade(0.4)
+            ]),u_min=-0.5,u_max=0.5, v_min=-0.5,v_max=0.5).scale(5).shift([0,1,2.5]).set_color(TEAL).fade(0.4)
         
         c = Circle().set_color('#FF00FF').shift([-0.4,0,1.5]).rotate(1.9,UP).scale(0.7)
 
@@ -26,10 +30,11 @@ class firstScene(ThreeDScene):
         max_text = TextMobject("maximum over $g(x,y)=k$",color = '#FFA074').shift([-1.7,0,0]).scale(0.5).shift(2.2*UP)
         min_text = TextMobject("minimum over $g(x,y)=k$",color = '#FFA074').shift([2.5,0.5,1]).scale(0.5).shift(0.5*UP)
         label_f = TextMobject("$z=f(x,y)$",color = '#8A2BE2').scale(0.5).shift(3*UP+3*RIGHT)
-        label_g = TextMobject("$g(x,y)=k$",color = '#8A2BE2').scale(0.5).shift(2*RIGHT)      
-       
+        label_g = TextMobject("$g(x,y)=k$",color = '#8A2BE2').scale(0.5).shift(2*RIGHT)       
 
         self.add(axes)
+        self.add(label_x)
+        self.add(label_y)
         self.set_camera_orientation(phi=75*DEGREES,theta=45*DEGREES)
         self.play(Write(surface)) 
         self.add_fixed_in_frame_mobjects(label_f)
@@ -49,5 +54,3 @@ class firstScene(ThreeDScene):
         self.play(Write(maxima_refl))
         self.play(Write(minima_refl))
         self.wait(1)
-
-