Question: Maple did not find the correct answer

Me or Maple?

Okay here's the problem.  A function is described as Y:={a*t^2*[exp^(-b*t)]*cos(c*t)}/(1+d*sqrt(t));

I differentiate Y wrt t to find the velocity of the funtion V:= diff(Y,t);  also acceleration A:=diff(Y,t,t);

I give some values to a,b,c,d and assign a T:=20  and so a:=2: b:=3/8: c:=10: d:=1

Now I plot to view the velocity of the function over the time t=0..T    plot(V,t=0..T);  GREAT!

Now I want to solve the function and find at what time t has the maximum velocity.  From the graph it occurs somewhere between 4 and 6 seconds.  TMAX:=fsolve(A=0,t=4..6); and the answer maple gives is TMAX:=4.868771376.  

okay so I find the velocity at that point VMax:=eval(V,t=TMAX);  answer is 23.81789390  .... WRONG!!!

Okay by looking at the graph I see that the peak at around 4.24 looks higher.   To find out I eval(V,t=4.24); and the answer I get is 23.966...  higher than the maximum maple gave me.  So right now I don't have a lot of faith in maple giving me the correct answers. 

So what gives?  Hopefully someone can point out something I did wrong.  If not then why didn't Maple find the highest point of velocity? 


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