Function 3

Function 2

Function 1

Function 4

Click and drag point A

Function 5

Select a function

0

Local slope at A 

f(x)

slope
f'(x)

aq = 0.15
c = 1
b = -1
linear(x) = -1 + 0.85 * x
m = false
i = false
h = true
a = 0.3
e = 2.718281828459045
poly(x) = (8 * x - x^(2) + 0.15 * x^(3) - 0.025 * x^(5) + 0.0010 * x^(8)) * e^(-x)
d = 10
sat(x) = d * (1 - e^(-a * x))
k = 0.05
gauss(x) = d * e^(-k * x^(2))
q(x) = aq * x^(2) + b * x + c
n = false
decay(x) = d * e^(-a * x / 2)
xp(x) = e^(a * x / 2)
f = If(x ≥ 0, If[h, linear, If[i, q, If[m, sat, If[n, gauss, poly]]]])
O: (0, f(0))
A = Point(f)
t = Tangent(A, f)
s = Slope(t)
avgslope: (y(A) - y(O)) / x(A)
B = (18.368087183547676, 4.462729033006186)
C: (x(B), y(B) + avgslope)
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)
I: (x(F), y(F) + s)
v = Segment(F, I)
axoff = 9
SO: (0, -axoff)
S1: (1, -axoff)
g = Ray(SO, S1)
slopescale = 0.1
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))
Scale = 2 (slider from 0.1 to 5, step 0.1)
S: (x(A), -axoff + Scale * s)
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))
o = false
Axoff = 4
J = Intersect(yt4n, yAxis)
l = Ray(SO, J)
p = Line(A, S)
K = Intersect(p, g)
r = Segment(S, K)
syax = Segment(SO, (x(SO), y(SO) + 0.8 * axoff))