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from manimlib.imports import *
class vedio(Scene):
def construct(self):
"""
视频封面
"""
title = TextMobject("数学暑假作业(2) 函数的应用 第17题")
title.scale(1.5)
author = TextMobject("讲解：华昊辉")
author.shift(DOWN)
self.play(Write(title), Write(author))
self.wait(2)
self.clear()
"""
题目，导入
"""
que1 = TexMobject(r"\text{17.已知函数}",
r"f(x)=x^2+mx-1",
r"\text{，对于任意}",
r"x\in[m, m+1]")
que2 = TexMobject(r"\text{都有}",
r"f(x) < 0",
r"\text{成立，求}",
r"\text{实数}",
r"m",
r"\text{的取值范围}")
que1.shift(UP * 3 + LEFT * 0.65)
que2.shift(UP * 3 + LEFT * 2.5 + DOWN)
self.play(Write(que1), Write(que2))
self.wait(13)
self.play(ApplyMethod(que1[1].set_color, TEAL_C), ApplyMethod(que1[3].set_color, TEAL_C),
ApplyMethod(que2[1].set_color, TEAL_C),
ApplyMethod(que2[3].set_color, TEAL_C), ApplyMethod(que2[4].set_color, TEAL_C))
self.wait(9)
self.clear()
"""
解析函数图像
"""
mt = TextMobject('$m =$')
mt.shift(UR * 3)
m = DecimalNumber(-2).scale(2)
dm = m.get_value()
m.scale(0.45)
m.next_to(mt)
axes = Axes(
number_line_config={"color": LIGHT_GREY,
"include_tip": True,
"exclude_zero_from_default_numbers": True,
},
x_min=-10, x_max=6,
y_min=-7, y_max=3.5,
center_point=ORIGIN
)
axes.add_coordinates()
self.add(axes.get_axis_labels())
func = FunctionGraph(
lambda x: x ** 2 + dm * x - 1,
)
funcf = FunctionGraph(
lambda x: x ** 2 + 2 * x - 1,
)
l1 = Line(np.array([dm, 7, 0]), np.array([dm, -7, 0]))
l2 = Line(np.array([dm + 1, 10, 0]), np.array([dm + 1, -10, 0]))
l1f = Line(np.array([2, 7, 0]), np.array([2, -7, 0]))
l2f = Line(np.array([2 + 1, 10, 0]), np.array([2 + 1, -10, 0]))
l1.set_color(RED)
l2.set_color(RED)
l1f.set_color(RED)
l2f.set_color(RED)
m.set_color(BLUE)
mt.set_color(BLUE)
self.play(Write(axes),
Write(func),
Write(l1),
Write(l2),
Write(mt),
Write(m))
self.wait(21)
self.play(ChangeDecimalToValue(m, 2),
ReplacementTransform(l1, l1f),
ReplacementTransform(l2, l2f),
ReplacementTransform(func, funcf),
run_time=10, rate_func=linear)
self.clear()
"""
解题
"""
self.add(que1, que2)
self.wait(61)
r1 = TexMobject(r"f(m)=m^2+m^2-1<0")
r2 = TexMobject(r"f(m+1) = (m+1)^2 + m(m+1) - 1 < 0")
r = TextMobject("综上，解得：$-\\frac{\\sqrt{2}}{2}<m<0$")
r.shift(DOWN * 2)
r2.shift(DOWN)
self.play(Write(r1), Write(r2), run_time=6)
self.wait(2)
r1f = TextMobject("$-\\frac{\\sqrt{2}}{2}<m<\\frac{\\sqrt{2}}{2}$")
r2f = TextMobject("$-\\frac{3}{2}<m<0$")
r2f.shift(DOWN)
self.play(ReplacementTransform(r1, r1f), ReplacementTransform(r2, r2f), Write(r))
self.wait(5)
self.clear()
"""
结束
"""
ty = TextMobject("谢谢观看！")
self.play(Write(ty), ApplyMethod(ty.scale, 1.5))
self.wait(2)
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