surfer
Date: 7 December 2013

Gradient of the function at one point = surfboard direction

The Workings:

Title

f(x) = ((((-0.12) * x^(3)) + (0.65 * x^(2)) - (0.94 * x) + 0.6) * 1.8) + 1
S = Point(f)
q = Circle(S, 0.28)
a = Tangent(S, f)
O, P = Intersect(q, a)
B = Point(a)
B' = Mirror(B, S)
b = Segment(P, O)
c = OrthogonalLine(S, b)
D = Point(c)
E = Point(c)
G = Point(b)
G' = Mirror(G, c)
H = Midpoint(B, B')
d = Circle(S, 0.1)
e = Circle(S, 0.3)
g = Circle(S, 0.6)
C = Intersect(d, c, 2)
F = Intersect(e, c, 2)
I = Intersect(g, c, 2)
K = Point(b)
j = Segment(C, K)
L = Point(b)
k = Segment(C, L)
p = Circle(F, 0.2)
h = Circle(I, 0.1)
J = Intersect(h, c, 1)
i = OrthogonalLine(F, c)
M = Intersect(p, i, 2)
N = Intersect(p, i, 1)
l = Segment(M, N)
m = Segment(I, C)
n = Segment(P, O)
o = Integral(f, -0.2, 4)
z: (y(B) - y(S)) / (x(B) - x(S))
T = Intersect(b, n)
r: y(B)
s: y(S)
t: x(B)
u: x(S)
text3: "$\frac{y(B)-y(A)}{x(B)-x(A)}$
$=\frac{" + (LaTeX[r]) + "-" + (LaTeX[s]) + "}{" + (LaTeX[t]) + "-" + (LaTeX[u]) + "}$
$=" + (LaTeX[z]) + "$"
text2: "Surfboard Number = " + z + ""
v = true
w = true