title: Maple, maximum value of a numeric function
body: <p>I am trying to compute the maximum value of the solution of a system with two ODEs using Maple. I have firstly solved the system itself:</p>
  
  <pre><code>&gt; with(DEtools):with(plots):
  &gt; a1:=0.00875;a2:=0.075;b1:=7.5;b2:=2.5;d1:=0.0001;d2:=0.0001;g:=4*10^(-8);K1:=5000;K2:=2500;n:=2;m:=2;
  
  &gt; dsol:= dsolve({
  diff( x(t), t ) = a1+b1*x(t)^n/(K1^n+x(t)^n)-g*x(t)*y(t)-d1*x(t), 
  diff( y(t), t ) = a2+b2*x(t)^m/(K2^m+x(t)^m)-d2*y(t), 
  x(0) = 1000, y(0) = 1000}, numeric, output = listprocedure);
  
  &gt; xt:= eval( x(t), dsol );
  yt:= eval( y(t), dsol );
  
  
  &gt; X:=plot(xt(t),t=0..50000,color=blue,legend="x(t)"):
  Y:=plot(yt(t),t=0..50000,color=green,legend="y(t)"):
  &gt; display([X,Y]);
  </code></pre>
  
  <p>I got the solutions of the system on xt and yt, but they are numeric solutions. Therefore, the function of Maple maximize() does not work:</p>
  
  <pre><code>&gt; maximize(xt);
  &gt; maximize(xt(t),t=0..20000);
  </code></pre>
  
  <p>Is it possible to compute the maximum value of a numeric function with Maple?</p>