(x_0+Δx,f(x_0+Δx))

(x_0,f(x_0))

Δx=%v

f(x)=

x_0=

show limit for Δx=0

Δx=

dxsegheightmult = -0.05
dxsegheightbase = 0.09
f(x) = x^(2)
height: y(Corner[3]) - y(Corner[2])
B = Point(f)
A = Point(f)
width: x(Corner[2]) - x(Corner[1])
dx = 1 (slider from -5 to 5, step width / 200)
dy: y(B) - y(A)
inputBox1 = Textfield(f)
a = Line(A, B)
dydx = If(dx ≠ 0, dy / dx, NaN)
C: (x(B), y(A))
E: (x(B), y(A) + If[y(B) < y(A), 1, -1] * height / 20)
F: (x(B) + If[x(B) ≥ x(A), 1, -1] * width / 30, y(A))
G: (x(B) + If[x(B) ≥ x(A), 1, -1] * width / 30, y(B))
D: (x(A), y(A) + If[y(B) < y(A), 1, -1] * height / 20)
H: (D + E) / 2
poly1, a_1, b, c = Polygon(B, C, A)
d = Segment(D, E)
e = Segment(F, G)
x0 = 0.3
inputBox3 = Textfield(x0)
y0: y(A)
y1: y(B)
text5: "$ \frac{\Delta y}{\Delta x}=\frac{" + (LaTeX[dy]) + "}{" + (LaTeX[dx]) + "}=" + (LaTeX[dydx]) + " $"
text1: "$ \Delta x = " + (LaTeX[dx]) + " $"
text6: "$  \Delta y = " + (LaTeX[dy]) + "$"
text4: "$ \Delta y = f(x_0+\Delta x)-f(x_0)=" + (LaTeX[y1]) + "-" + (LaTeX[y0]) + " =" + (LaTeX[dy]) + "$"
showderiv = false
fprime: f'(x0)
text2: "$\frac{dy}{dx}= \lim_{\Delta x \to 0}\frac{\Delta y}{\Delta x} =" + (LaTeX[fprime]) + "$"
I: (F + G) / 2
text3: "$\Delta y=" + (LaTeX[dy]) + " $"
text7: "$ \Delta x=" + (LaTeX[dx]) + " $"
dxsegheight: dxsegheightbase + dxsegheightmult * height
h: y = dxsegheight
J = Point(h)
inputBox2 = Textfield(dx)
fx0: f(x0)
g: y = fx0 + fprime * (x - x0)