The Meaning of the Derivative

f(x+h)

f(x)

Tangent at the point P

h

\theta

Slope of the red chord

P

Q

P = Q

\frac{f(x+h)-f(x)}{h} = 

f(x) = (x + 3) * (x - 1)
P: (2, f(2))
h = 2 (slider from 0 to 2, step 0.1)
Q: (x(P) + h, f(x(P) + h))
a = OrthogonalLine(Q, xAxis)
A = Intersect(a, xAxis)
b = Segment(Q, A)
c = OrthogonalLine(P, b)
B = Intersect(b, c)
d = Segment(P, B)
e = Segment(Q, B)
C: (x(Q) + 0.2, y(Q))
D: (x(Q) + 0.2, 0)
E = Midpoint(C, D)
F: (x(P) - 0.2, y(P))
G: (x(F), 0)
H = Midpoint(F, G)
j = Tangent(P, f)
I = Midpoint(P, B)
k = Line(P, Q)
u = Vector(C, D)
v = Vector(D, C)
w = Vector(F, G)
z = Vector(G, F)