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from manimlib.imports import*
import math as m
#---- case 1: parial derivatives exist at critical point 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
#---- f(x,y) = e^(-10x^2-10y^2)
surface = ParametricSurface(
lambda u, v: np.array([
u,
v,
m.exp(-10*u**2-10*v**2)
]),u_min = -1, u_max = 1, v_min = -1, v_max = 1, checkerboard_colors = [TEAL_E,TEAL_D,TEAL_C,TEAL_B]).fade(0.6).scale(3.5).shift([0,0,1.5])
l1 = Line([0,0,3.75],[0,0,0],color = '#800000')
d = Dot([0,0,3.75],color = '#800000') #---- critical point
d_text = TextMobject("$\\frac{\\partial f}{\\partial x}=\\frac{\\partial f}{\\partial y} = 0$").scale(0.8).to_corner(UL)
f_text = TextMobject("Critical Point ",color = YELLOW).shift(3.4*UP).scale(0.5)
self.set_camera_orientation(phi = 45*DEGREES, theta = 40*DEGREES)
self.add(axes)
self.add(label_x)
self.add(label_y)
self.add_fixed_in_frame_mobjects(d_text)
self.begin_ambient_camera_rotation(rate = 0.2)
self.play(Write(surface))
self.wait(1)
self.play(Write(l1))
self.play(Write(d))
self.wait(1)
self.add_fixed_in_frame_mobjects(f_text)
self.wait(3)
self.play(FadeOut(f_text),FadeOut(surface),FadeOut(axes),FadeOut(d_text),FadeOut(d),FadeOut(l1),FadeOut(label_x),FadeOut(label_y))
#---- case 2: parial derivatives do not exist at critical point 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
#---- g(x,y)= |x|+|y|
surface = ParametricSurface(
lambda u, v: np.array([
u,
v,
abs(u)+abs(v)
]),u_min = -1.5, u_max = 1.5, v_min = -1.5, v_max = 1.5, checkerboard_colors = [TEAL_E,TEAL_D,TEAL_C,TEAL_B])
d2 = Dot([0,0,0],color = '#800000') #---- critical point
d2_text = TextMobject("$\\frac{\\partial f}{\\partial x}$ and/or $\\frac{\\partial f}{\\partial y}$ does not exist").scale(0.7).to_corner(UL)
g_text = TextMobject("Critical Point",color = YELLOW).shift(1.2*RIGHT).scale(0.6)
self.set_camera_orientation(phi = 60*DEGREES, theta = 40*DEGREES)
self.add(axes)
self.add(label_x)
self.add(label_y)
self.add_fixed_in_frame_mobjects(d2_text)
self.begin_ambient_camera_rotation(rate = 0.2)
self.wait(1)
self.play(Write(surface2))
self.wait(1)
self.play(Write(d2))
self.wait(1)
self.add_fixed_in_frame_mobjects(g_text)
self.wait(2)
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