MuPAD Pro Computing Essentials - Examples 

Example 12.2 - Local minimum and maximum values  

A typical undergraduate mathematics problem is to obtain the plot of a function and its derivative or derivatives on the same graph and investigate the existence of local minimum and maximum values. In this example, we will produce a graph of the function: 

We will start by declaring our function and its derivative. Then we will get a plot of both of them. 

• z := t -> (1 - t^3)/(1 + t^4);

• u := t -> diff(z(t), t);

• export(plot, Function2d):
  
  z1 := Function2d(z(t), t=-5..5,
     Color=RGB::Blue,
     LineWidth=15
  ):
    
  u1 := Function2d(u(t), t=-5..5):
    
  plot(z1, u1)

• solutions := solve(u(t)=0, t);

• solutions := float(solutions);

	{1.784357981, - 0.5459265692 + 1.45937795 I,

	- 0.5459265692 - 1.45937795 I, -0.6925048426, 0.0}

• rsol := solutions intersect Dom::Interval(-5,5)

• rsol:= [op(rsol)]

• Z1 := [rsol[1], subs(z(t), t=rsol[1])];
  Z2 := [rsol[2], subs(z(t), t=rsol[2])];
  Z3 := [rsol[3], subs(z(t), t=rsol[3])];

• export(plot, Point):
     
  P1 := Point(Z1):
  P2 := Point(Z2):
  P3 := Point(Z3):
    
  plot(z1, u1, P1, P2, P3,
     PointWidth=60,
     PointStyle=FilledCircles
  )

 NOTE: this example is quite complicated to copy it into your notebook. For this purpose I included here a complete  MuPAD notebook.  Download it, open in MuPAD and then execute all commands.