f(x) = a·x5 + b·x4 + c·x3 + d·x2 + e·x + g
Bedingungen
f(0) = 0 --> g = 0
f'(0) = 0 --> e = 0
f''(0) = 0 --> d = 0
f(5) = 2 --> 3125·a + 625·b + 125·c = 2
f'(5) = TAN(40°) --> 3125·a + 500·b + 75·c + 10·d + e = TAN(40°)
f''(5) = 0 --> 2500·a + 300·b + 30·c + 2·d = 0
Lösung
a = -0.0001877 ∧ b = -0.001010 ∧ c = 0.02574 ∧ d = 0 ∧ e = 0 ∧ g = 0
Skizze
Plotlux öffnen f1(x) = 0f2(x) = tan(40·π/180)·(x-5)+2f3(x) = -0,0001877x5-0,001010x4+0,02574x3Zoom: x(-1…8) y(-1…5)