Slope linear in x

Slope proportional to x

Constant slope

Slope inversely proportional to x

Slope proportional to f(x)

Click and drag point A

Select a slope function

Slope proportional to -f(x)

0

f(x)

Slope
f'(x)

d = 10
Offset = 0 (slider from -5 to 5, step 0.1)
inverse(x) = log(x)
c = 1
linear(x) = 0.85 * x
aq = 0.15
q1(x) = aq * x^(2)
b = -1
q(x) = aq * x^(2) + b * x + c
m = false
i = false
h = true
n = false
a = 0.3
decay(x) = d * ℯ^(-a * x / 2)
xp(x) = ℯ^(a * x / 2)
o = false
sinverse(x) = 1 / x
sdecay(ggbtmpvarggbtmpvarggbtmpvarggbtmpvarggbtmpvarggbtmpvarggbtmpvarggbtmpvarggbtmpvarggbtmpvarggbtmpvarggbtmpvarggbtmpvarggbtmpvarggbtmpvarggbtmpvarggbtmpvarggbtmpvarggbtmpvarggbtmpvarggbtmpvarggbtmpvarggbtmpvarggbtmpvarggbtmpvarggbtmpvarggbtmpvarggbtmpvarggbtmpvarggbtmpvarggbtmpvarggbtmpvarggbtmpvarggbtmpvarggbtmpvarggbtmpvarggbtmpvarggbtmpvarggbtmpvarggbtmpvarggbtmpvarggbtmpvarggbtmpvarggbtmpvarggbtmpvarggbtmpvarggbtmpvarggbtmpvarggbtmpvarggbtmpvarggbtmpvarggbtmpvarggbtmpvarggbtmpvarggbtmpvarggbtmpvarggbtmpvarggbtmpvarggbtmpvarggbtmpvarggbtmpvarggbtmpvarggbtmpvarggbtmpvarggbtmpvarggbtmpvarggbtmpvarggbtmpvarggbtmpvarggbtmpvarggbtmpvarggbtmpvarx) = -2 * ℯ^(-a * ggbtmpvarggbtmpvarggbtmpvarggbtmpvarggbtmpvarggbtmpvarggbtmpvarggbtmpvarggbtmpvarggbtmpvarggbtmpvarggbtmpvarggbtmpvarggbtmpvarggbtmpvarggbtmpvarggbtmpvarggbtmpvarggbtmpvarggbtmpvarggbtmpvarggbtmpvarggbtmpvarggbtmpvarggbtmpvarggbtmpvarggbtmpvarggbtmpvarggbtmpvarggbtmpvarggbtmpvarggbtmpvarggbtmpvarggbtmpvarggbtmpvarggbtmpvarggbtmpvarggbtmpvarggbtmpvarggbtmpvarggbtmpvarggbtmpvarggbtmpvarggbtmpvarggbtmpvarggbtmpvarggbtmpvarggbtmpvarggbtmpvarggbtmpvarggbtmpvarggbtmpvarggbtmpvarggbtmpvarggbtmpvarggbtmpvarggbtmpvarggbtmpvarggbtmpvarggbtmpvarggbtmpvarggbtmpvarggbtmpvarggbtmpvarggbtmpvarggbtmpvarggbtmpvarggbtmpvarggbtmpvarggbtmpvarggbtmpvarggbtmpvarx / 2)
sexp(x) = ℯ^(a * x / 2)
sq1(x) = 2 * aq * x
sq(x) = b + 2 * aq * x
axoff = 9
slinear(x) = 0.85
Scale = 2 (slider from 0.1 to 5, step 0.1)
e = 2.718281828459045
poly(x) = (8 * x - x^(2) + 0.15 * x^(3) - 0.025 * x^(5) + 0.0010 * x^(8)) * e^(-x)
k = 0.05
gauss(x) = d * e^(-k * x^(2))
sgauss(x) = -2 * k * x * gauss(x)
spoly(x) = (8 - 2 * x + 0.45 * x^(2) - 0.15 * x^(4) - poly(x)) * ℯ^(-x)
slopescale = 0.1
sat(x) = d * (1 - e^(-a * x))
slope(x) = -axoff + Scale * If[x ≥ 0, If[h, slinear, If[i, sq1, If[m, sq, If[n, sinverse, If[o, sexp, sdecay]]]]]]
A = Point(slope)
B = (20.195844192472126, 4.462729033006186)
D: (x(B) - 0.5, y(B))
E: (x(B) + 0.5, y(B))
F: (x(B) + 1, y(B))
G: (x(F) - 0.5, y(F))
H: (x(F) + 0.5, y(F))
j = Segment(G, H)
SO: (0, -axoff)
S1: (1, -axoff)
g = Ray(SO, S1)
t1 = Segment((2, -axoff), (2, -axoff - 0.1))
t4 = Segment((4, -axoff), (4, -axoff - 0.1))
t6 = Segment((6, -axoff), (6, -axoff - 0.1))
t8 = Segment((8, -axoff), (8, -axoff - 0.1))
t10 = Segment((10, -axoff), (10, -axoff - 0.1))
t12 = Segment((12, -axoff), (12, -axoff - 0.1))
t14 = Segment((14, -axoff), (14, -axoff - 0.1))
t16 = Segment((16, -axoff), (16, -axoff - 0.1))
yt2 = Segment((0, -axoff + 2 * Scale), (-0.1, -axoff + 2 * Scale))
yt4 = Segment((0, -axoff + 4 * Scale), (-0.1, -axoff + 4 * Scale))
yt6 = Segment((0, -axoff + 6 * Scale), (-0.1, -axoff + 6 * Scale))
yt6n = Segment((0, -axoff - 6 * Scale), (-0.1, -axoff - 6 * Scale))
yt4n = Segment((0, -axoff - 4 * Scale), (-0.1, -axoff - 4 * Scale))
yt2n = Segment((0, -axoff - 2 * Scale), (-0.1, -axoff - 2 * Scale))
Axoff = 4
f(x) = Offset + If[x ≥ 0, If[h, linear, If[i, q1, If[m, q, If[n, inverse, If[o, xp, decay]]]]]]
S: (x(A), f(x(A)))
p = false
C = Point(yAxis)
l = Ray(SO, C)
slopeyax = Segment(SO, (x(SO), y(SO + 0.8 * axoff)))
r = Line(S, A)
slope2 = If(slope(x) < -0.2 * axoff, slope)