h

\Delta f=2h^2+4h

y=4x-2 \ equazione  \ retta \ tangente

f(x)=2x^2

B

A

f(x) = (2 * x^(2))
f' = Derivative(f)
A = Point(f)
g = OrthogonalLine(A, xAxis)
J = Intersect(g, xAxis)
j = Segment(A, J)
x_0: x(Intersect[j, xAxis])
B = Point(f)
b = Tangent(A, f)
a = Line(A, B)
E = Point(xAxis)
F = Point(yAxis)
e = OrthogonalLine(A, yAxis)
H = Intersect(e, yAxis)
c = OrthogonalLine(B, xAxis)
d = OrthogonalLine(B, xAxis)
M = Intersect(d, xAxis)
i = OrthogonalLine(A, d)
C = Intersect(d, i)
k = Segment(A, C)
l = Segment(B, M)
m = OrthogonalLine(B, yAxis)
D = Intersect(m, yAxis)
n = Segment(D, B)
h: x(M) - x(J)
delta_f: f(x_0 + h) - f(x_0)
deriv_f: f'(x_0)
rappincr: delta_f / h
testo8: "" + (LaTeX[x_0]) + ""
testo2: "" + (LaTeX[x_0]) + "+h"
testo4: "f(" + (LaTeX[x_0]) + "+h)=2(" + (LaTeX[x_0]) + "+h)^2"
y_0: f(x_0)
testo3: "f(" + (LaTeX[x_0]) + ")=" + (LaTeX[y_0]) + ""
testo1: "Spostando\ i\ punti \ A \ o \ B\ confronta\ i\ valori \\ del\ RAPPORTO\ INCREMENTALE  \frac{\Delta f}{h}\ con\\la\ DERIVATA \\
f'(x_0)=\lim_{x→x_0}\frac{f(x_0+h)-f(x_0)}{h}=\lim_{x→x_0}\frac{\Delta f}{h}= " + (LaTeX[deriv_f]) + "   \\ 
x_0=" + (LaTeX[x_0]) + "\\
h=" + (LaTeX[h]) + "   \\ \Delta f=" + (LaTeX[delta_f]) + "  \\ \frac{\Delta f}{h}=" + (LaTeX[rappincr]) + "  \\"