t

\frac{dz}{dt}

t

z

ymin1 = -2.01364858819627
ymax1 = 4.735289310597245
yscale: ymax1 - ymin1
threshold = 0.03
xmax1 = 8.327694482932833
xmin1 = -0.9665273004237986
xscale: xmax1 - xmin1
threshold_x: (threshold * xscale)
threshold_y: (threshold * yscale)
xlabel1displayed: "" + (LaTeX[xlabel1]) + ""
ylabel1displayed: "" + (LaTeX[ylabel1]) + ""
ymax2 = 3.7009455060887864
ymin2 = -0.8342723466210138
LL1 = Corner(1, 1)
UR1 = Corner(1, 3)
LL2 = Corner(2, 1)
UR2 = Corner(2, 3)
xmax2 = 7.853296703296702
xmin2 = -1.0711538461538461
xlabel2displayed: "" + (LaTeX[xlabel2]) + ""
ylabel2displayed: "" + (LaTeX[ylabel2]) + ""
f(x) = ((((1 / 5 * (x - 1)) * (x - 3)) * (x - 6)) * (1 - (x - 3)^(2) / 20 + (x - 3)^(4) / 800 - (x - 3)^(6) / 48000 + (x - 3)^(8) / 3840000 - (x - 3)^(10) / 384000000))
f1(x) = If[0 ≤ x ≤ Infinity,f(x)]
g(x) = ((-x^(14))) / 26880000000 + x^(13) / 624000000 - (79 * x^(12) / 2880000000) + (2359 * x^(11) / 10560000000) - (3397 * x^(10) / 3840000000) + (40153 * x^(9) / 8640000000) - (6137 * x^(8) / 128000000) + (9263 * x^(7) / 160000000) + (6044159 * x^(6) / 3840000000) + (347093 * x^(5) / 160000000) - (9959083 * x^(4) / 160000000) - (14738483 * x^(3) / 192000000) + (1762778079 * x^(2) / 1280000000) - (734535153 * x / 320000000)
y0 = 1.3
g1(x) = If[0 ≤ x ≤ Infinity,g(x) - g(0) + y0]
step = 6 (slider from 1 to 7, step 1)
fzeros: {Roots[f, 0, xmax1]}
veclen = 0.5
vecheight = 1
fzerosx = Zip(x(a), a, fzeros)
fzerolines = Zip(x = a, a, fzerosx)
fzeroxextend = Append(Append[0, fzerosx], xmax2)
midpoints: (First[fzeroxextend, 4] + Last[fzeroxextend, 4]) / 2
vecshift = -0.2
dirvecs = Zip(Vector[(a + vecshift, 0), (a + vecshift + veclen, (If[f(a) > 0, 1, -1] * vecheight))], a, midpoints)
gdraw = 1 (slider from 0 to 1, step 0.05)
showstep = true
g2(x) = If[0 ≤ x ≤ (x(Corner[2, 2]) * gdraw),g1(x)]
horizvecs = Zip(Vector[(a + vecshift, 0), (a + vecshift + veclen, 0)], a, fzerosx)
dy = 0.1
Y0pt_sub = Point(yAxis)
Y0pt = DynamicCoordinates(Y0pt_sub, 0, (round(y(Y0pt_sub) / dy) * dy))
equationText: "\begin{align*}
\frac{dz}{dt} &= f(t)\\
z(0) &= " + y0 + "
\end{align*}"