x_0

x_0=

g(x_0)

g(x_0)

f(g(x_0))

x_0

h(x_0)

+

-

←

→

↑

↓

f(x)=

g(x)=

g(x) = x^(2)
gprime = Derivative(g)
x0 = 1.5822015739362683
f(x) = x^(2) / 4
fprime = Derivative(f)
gx0: g(x0)
fpgx0: fprime(gx0)
b = -1
d = 1
A = Point(xAxis)
inputBox1 = Textfield(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)
gpx0: gprime(x0)
hpx0: (gpx0 * fpgx0)
text2: "g'(x_0) = " + gpx0 + ""
text1: "f'(g(x_0)) = " + fpgx0 + ""
text3: "h'(x_0)=" + gpx0 + "·" + fpgx0 + "=" + hpx0 + ""
center = (1.5758427222616274, 1.7942536443148696)
height = 3.0000000000000004
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)
inputBox2 = Textfield(f)
inputBox3 = Textfield(g)
gx0tanlin(x) = gx0 + (gpx0 * (x - x0))
fgx0tanlin(x) = fgx0 + (fpgx0 * (x - gx0))
hx0tanlin(x) = fgx0 + (hpx0 * (x - x0))
text4: "$h(x)= " + (LaTeX[p]) + "$"