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from manimlib.imports import *
class derivative2(GraphScene, MovingCameraScene):
def setup(self):
GraphScene.setup(self)
MovingCameraScene.setup(self)
CONFIG = {
"y_max" : 100,
"y_min" : 0,
"x_max" : 10,
"x_min" : 0,
"y_tick_frequency" : 100,
"x_tick_frequency" : 10,
"axes_color" : WHITE,
"num_graph_anchor_points": 3000, #this is the number of points that graph manim
"graph_origin" : ORIGIN,
"x_labeled_nums": None,#list(range(0,11)),
"y_labeled_nums": None,#list(range(0,101))[::10],
"x_axis_label":"$x$",
"y_axis_label":"$f(x)$",
"x_axis_width": 5,
"y_axis_height": 5,
"start_x" : 2,
"start_dx" : 6,
"df_color" : YELLOW,
"dx_color" : GREEN,
"secant_line_color" : MAROON_B,
"zoomed_camera_frame_starting_position": ORIGIN+2*DOWN+6*LEFT,
}
def construct(self):
self.setup()
self.camera_frame.save_state()
self.graph_origin = ORIGIN+2*DOWN+6*LEFT
self.setup_axes()
graph23 = self.get_graph(lambda x : x**2+7, color = GREEN_SCREEN, x_min = 0, x_max = 10)
graph24 = self.get_graph(lambda x : x**2+7, color = GREEN_SCREEN, x_min = 8, x_max = 2.01)
line_1 = DashedVMobject(Line(np.array([-5,-2,0]), np.array([-5,-1.42,0])))
textdef = TextMobject("")
text1 = TexMobject("{ x }_{ 0 }").move_to(np.array([-5,-2.2,0]))
text2 = TextMobject("The line becomes tangential to the curve").move_to(self.graph_origin+RIGHT+0.5*UP).scale(0.01)
text3 = TexMobject(r"\frac { df }{ dx } =\frac { f({ x }_{ 0 }+h)-f({ x }_{ 0 }) }{ h-0 }").move_to(2*RIGHT)
text4 = TexMobject(r"\frac { df }{ dx } =\lim _{ h\rightarrow 0 }{ \frac { f({ x }_{ 0 }+h)-f({ x }_{ 0 }) }{ h } }").move_to(2*RIGHT)
squareobj = Square(side_length = 15).move_to(self.graph_origin+RIGHT+0.53*UP)
ss_group = self.get_secant_slope_group(
self.start_x, graph23,
dx = self.start_dx,
dx_label = "h",
df_label = "df",
df_line_color = self.df_color,
dx_line_color = self.dx_color,
secant_line_color = self.secant_line_color,
dot_df_top = True,
dot_dx_start = True,
dot_df_top_label = "Q",
dot_dx_start_label = "P",
secant_line_length = 8
)
self.play(ShowCreation(graph23))
self.wait()
self.play(ShowCreation(ss_group.secant_line))
self.add(text1)
self.play(ShowCreation(line_1))
self.wait(3)
self.play(ShowCreation(ss_group.dx_line))
self.play(ShowCreation(ss_group.dx_label))
self.play(ShowCreation(ss_group.df_line))
self.play(Write(ss_group.df_label))
self.play(ShowCreation(ss_group.dot_df_top), ShowCreation(ss_group.dot_dx_start))
self.play(ShowCreation(ss_group.dot_df_top_label), ShowCreation(ss_group.dot_dx_start_label))
self.wait()
self.play(ShowCreation(text3))
self.wait(2)
self.play(ReplacementTransform(text3, text4))
self.animate_secant_slope_group_change(ss_group, target_dx = 0.01, run_time = 5)
self.wait(2)
self.play(self.camera_frame.set_width,0.2,self.camera_frame.move_to,squareobj,run_time = 2)
self.wait()
self.play(ShowCreation(text2))
self.wait(3)
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