Lösungen/Solutions/I1S1Ue/Ex16

L=Lektion/Leçon-- Sprechstunde/heures de consultation
W=Work/Arbeit/Travail
A  =Anhang/  Annexe / Appendice

Ueb/Ex 1      W

f1[x_] := (x^x)^x;  D[f1[x], x]

Ueb/Ex 2      W

f2[x_] := x^(x^x);  D[f2[x], x]

Ueb/Ex 3      W

f3[x_] := 1/2 x  -   Cos[x] ;  
    D[f3[x], x]  // Simplify

D[f3[x], {x, 2}]

Solve[D[f3[x], x] == 0, {x}]

Solve[D[f3[x], {x, 2}] == 0, {x}]

Plot[f3[x], {x, -2 Pi, 2  Pi}];

Ueb/Ex 4      W

f4[x_] := x  Sqrt[x]; D[f4[x], x]

Solve[D[f4[x], x] == 0, {x}]

Plot[f4[x], {x, 0, 3}];

Ueb/Ex 5      W

f5[x_] := E^(-x^2); D[f5[x], x]

Plot[f5[x], {x, -3, 3}];

Solve[D[f5[x], x] == 0, {x}]

D[f5[x], {x, 2}]

Solve[D[f5[x], {x, 2}] == 0, {x}]

N[%]

Ueb/Ex 6      W

f6[x_] := 3  x^3 + 4  x^2 - 5  x - 5; D[f6[x], x]

Solve[D[f6[x], x] == 0, {x}]

N[%]

Solve[D[f6[x], {x, 2}] == 0, {x}]

N[%]

Plot[f6[x], {x, -3, 2}];

Ueb/Ex 7      W

f7[x_] := x^4 - x^2 - 1; D[f7[x], x]

Solve[D[f7[x], x] == 0, {x}]

N[%]

Solve[D[f7[x], {x, 2}] == 0, {x}]

N[%]

Plot[f7[x], {x, -3, 2}];