f(x)=e^x(x^2-2x+2-k^2)

Taylorpolynome

Ortskurven der Wendepunkte

Ortskurve der Extrema

Kurvenschar

CAS-Fenster lesen!

k = 0.9 (slider from -5 to 5, step 0.1)
f(x) = (ℯ^(x) * (x^(2) - (2 * x) + 2 - k^(2)))
E_1: ((-k), f((-k)))
E_2: (k, f(k))
W_1: (-1 + sqrt(1 + k^(2)), f(-1 + sqrt(1 + k^(2))))
g = TaylorSeries(f, x(E_1), 3)
h = TaylorSeries(f, x(E_2), 3)
p = TaylorSeries(f, x(W_1), 3)
Text1: "E_1 : " + (LaTeX[g]) + ""
Text2: "E_2 : " + (LaTeX[h]) + ""
Text3: "W_1 : " + (LaTeX[p]) + ""
W_2: (-1 - sqrt(1 + k^(2)), f(-1 - sqrt(1 + k^(2))))
Ortslinie1 = Locus(W_1, k)
Ortslinie2 = Locus(E_1, k)
Ortslinie3 = Locus(W_2, k)
Ws1: (0, 2)
Ws2: (-2, 1.3533)
f_s(x) = (exp(x) * (x^(2) - (2 * x) + 2))
a = false
b = false
c = false
l1 = Sequence((ℯ^(x) * (x^(2) - (2 * x) + 2 - k^(2))), k, 0, 1.7, 0.1)
d = true
A = (-2.74680141884872, 2.010132123975742)
B = (-2.229599173326586, 2.010132123975742)