moshtag

x

r.pilevar  ⧫⧫⧫  math-rp.ir

f(x) = If[-2 ≤ x ≤ 15, (-0.1 * (x - 10)^(2)) + 7]
g(x) = If[3 ≤ x ≤ 10, (-0.1 * (x - 10)^(2)) + 7]
A = Point(g)
B = Point(g)
h = Segment(B, A)
C = Point(h)
D = Point(h)
i = Segment(C, D)
a = Slope(i)
j = Tangent(A, g)
m = Slope(j)
B1: f
E: (0, y(B))
F: (0, y(A))
G: (x(A), 0)
H: (x(B), 0)
k = Segment(B, H)
l = Segment(A, G)
n = Segment(B, E)
p = Segment(F, A)
q = OrthogonalLine(A, k)
I = Intersect(q, k)
r = Segment(A, I)
s = Segment(B, I)
t = Segment(E, F)
text3: "f(b)-f(a)=" + (y(B) - y(A)) + ""
text1: "f(b)=" + r + ""
text2: "f(a)=" + l + ""
text4: "b-a=" + (x(B) - x(A)) + ""
text5: "\frac{f(b)-f(a)}{b-a}=\frac{" + (LaTeX[y(B) - y(A)]) + "}{" + (LaTeX[x(B) - x(A)]) + "}=" + (LaTeX[(y(B) - y(A)) / (x(B) - x(A))]) + ""
J = Point(k)
K = Point(r)