x_0

x_0=

g(x_0)

g(x_0)

f(g(x_0))

x_0

h(x_0)

a=

b=

c=

d=

+

-

←

→

↑

↓

a = 0.5
b = -1
c = 2
d = 1
g(x) = (a * x) + b
f(x) = (c * x) + d
A = Point(xAxis)
x0 = 4.110065552063405
inputBox1 = Textfield(x0)
gx0: g(x0)
B: (x0, gx0)
C: (0, gx0)
D: (gx0, 0)
fgx0: f(gx0)
E: (gx0, fgx0)
u = Vector(A, B)
F: (gx0, gx0)
v = Vector(B, F)
w = Vector(F, E)
i = Segment(D, F)
j = Segment(F, C)
h(x) = f(g(x))
G: (0, fgx0)
k = Segment(E, G)
H = Point(xAxis)
I: (x0, fgx0)
J: (0, fgx0)
z = Vector(H, I)
l = Segment(I, J)
ac: (a * c)
inputBox2 = Textfield(a)
inputBox3 = Textfield(b)
inputBox4 = Textfield(c)
inputBox5 = Textfield(d)
text2: "g'(x_0) = " + a + ""
text1: "f'(g(x_0)) = " + c + ""
text3: "h'(x_0)=" + a + "·" + c + "=" + ac + ""
text5: "$ f(x)=" + (LaTeX[f]) + " $"
text6: "$ g(x)=" + (LaTeX[g]) + " $"
center = (2.756682093416788, 3.4198250728862982)
height = 4.2857142857142865
width1: (height * x(Corner[1, 5]) / y(Corner[1, 5]))
width2: (height * x(Corner[2, 5]) / y(Corner[2, 5]))
maxx1: x(center) + width1
maxx2: x(center) + width2
minx1: x(center) - width1
minx2: x(center) - width2
maxy: y(center) + height
miny: y(center) - height
p = Simplify(h)
text7: "$h(x)=f(g(x))=" + (LaTeX[p]) + "$"