הגדרת הנגזרת
Author: גאולה

הגדרת הנגזרת כגבול של חותכים

שיפוע המשיק בנקודה A =

שיפוע החותך AB =

\frac{{x_A }^{2}-{ x_B }^{2}}{ x_A - x_B} =

f(x) = x^(2.0)
A = Point(f)
g = OrthogonalLine(A, xAxis)
D = Intersect(xAxis, g)
B = Point(f)
b = OrthogonalLine(B, xAxis)
B_2 = Intersect(b, xAxis)
d = Segment(B, B_2)
c = Tangent(A, f)
a = Segment(A, D)
C = Intersect(g, a)
e = Segment(A, B)
h = Slope(c)
text2: h + ""
i = Line(A, B)
j = Slope(i)
text4: j + ""
k: x(A)
text6: "\frac{{" + (x(A)) + "}^{2}-{" + (x(B)) + "}^{2}}{" + (x(A) + " -" + (x(B))) + "}"
E = (8.34146360543586, 6.755413399484704)
F = (8.305425928662672, 2.0559562204971966)
G = (3, 2)
H = (3.011781150272243, 6.770684695917837)
poly1, e_1, f_1, g_1, h_1 = Polygon(E, F, G, H)
A1 = 0
B1 = 0
A2 = 0.24906479555080593
B2 = 0.06203327238276476
A3 = 0.42954375339693
B3 = 0.18450783608232263
A4 = 0.6100227112430541
B4 = 0.37212770823232655
A5 = 0.6794376950300249
B5 = 0.46163558142771316
A6 = 0.8043846658465723
B6 = 0.6470346906491018
A7 = 0.8321506593613607
B7 = 0.6924747198755473
A8 = 0.8460336561187548
B8 = 0.7157729472856674
A9 = 0.8599166528761489
B9 = 0.7394566498937192
A10 = 0.8737996496335431
B10 = 0.7635258276997026
A11 = 0.8876826463909373
B11 = 0.7879804807036178
A12 = 0.9015656431483314
B12 = 0.8128206089054645
A13 = 1
B13 = 1
A14 = 1.123693591266638
B14 = 1.262687287053714
A15 = 1.4152365231719153
B15 = 2.002894416519731
A16 = 2.0677373707694406
B16 = 4.275537834476519
A17 = 2.428695286461689
B17 = 5.898560794481225
A18 = 2.49811027024866
B18 = 6.240554922321833
A19 = 2.5397592605208423
B19 = 6.450377101401376
C1: j
C2: j
C3: j
C4: j
C5: j
C6: j
C7: j
C8: j
C9: j
C10: j
C11: j
C12: j
C13: j
C14: j
C15: j
text7: "=  " + j
text8: "הנגזרת של הפונקציה " + f + " בנקודה בה x = " + (x(A))
text9: "f' (" + (x(A)) + " ) = " + h