Lösungen/ Solutions

Probl/Ex 1      W

p[x_] :=  (x + 1) (x - 4) (x - 5) // Expand;   p[
      x]

Plot[p[x], {x, -1.5, 6}];

D[p[x], x]

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

Solve[D[p[x] == 0, x], {x}] // N

Plot[{p[x], p'[x]}, {x, -1.5, 6}];

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

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

Solve[D[p[x], {x, 2}] == 0, {x}] // N

plot1 = 
        Plot[{p[x], p'[x], p''[x]}, {x, -1.5, 6}, 
          Epilog -> {Line[{{2.66, -20}, {2.66, 20}}],  
              Line[{{0.8107, -20}, {0.8107, 25}}],  
              Line[{{4.52, -20}, {4.52, 20}}]}];

Probl/Ex 2      W

f[x_] := -x^2 + 1

A[
        x_] := 2 x f[x]  +  2 *1/2 x (f[0] - f[x]) // 
          Simplify // Expand; A[x]

D[A[x], x]

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

Solve[D[A[x] == 0, x], {x}] // N

Probl/Ex 3      W

f1[x_] := (Cos[x])^2;  f2[x_] := (Cos[x])^3;

d[x_] :=  f1[x] - f2[x]

D[d[x], x]

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

% // N

Plot[Evaluate[{d[x], D[d[x], x]}], {x, 0, Pi/2}];

Probl/Ex 4      W

A[fi_] := 2 Cos[fi]*1 + 2 1/2  Cos[fi]  Sin[fi];  
    A[fi]

D[A[fi], fi]

Solve[D[A[fi], fi] == 0, {fi}]

% // N

Plot[Evaluate[{A[fi], D[A[fi], fi]}], {fi, 0, Pi/2}];