x_4=

f(x_4)=

x_0 = -4.02 (slider from -10 to 10, step 0.01)
e = -1.4 (slider from -5 to 5, step 0.1)
d = 0.40000000000000036 (slider from -5 to 5, step 0.1)
c = 0.5 (slider from -5 to 5, step 0.1)
b = 0 (slider from -5 to 5, step 0.1)
a = 0 (slider from -5 to 5, step 0.1)
f(x) = a x^(4) + b x^(3) + c x^(2) + d x + e
g(x) = f'(x_0) x + f(x_0) - f'(x_0) x_0
X_1 = Intersect(g, xAxis, 1)
h(x) = f'(x(X_1)) x + f(x(X_1)) - f'(x(X_1)) x(X_1)
X_2 = Intersect(h, xAxis, 1)
α(x) = f'(x(X_2)) x + f(x(X_2)) - f'(x(X_2)) x(X_2)
X_3 = Intersect(α, xAxis, 1)
β(x) = f'(x(X_3)) x + f(x(X_3)) - f'(x(X_3)) x(X_3)
X_4 = Intersect(β, xAxis, 1)
s: x(X_4)
X_0: (x_0, 0)
A: (x_0, f(x_0))
B: (x(X_1), f(x(X_1)))
i = Segment(X_1, B)
C: (x(X_2), f(x(X_2)))
j = Segment(X_0, A)
k = Segment(X_2, C)
D: (x(X_3), f(x(X_3)))
l = Segment(D, X_3)
text1: s + ""
z: f(x(X_4))
text3: z + ""