Maximum value - Solution
y(t)=200*t-t^2 for 0<=t<400 with a sampling interval of 0.05.
t represents the length of one side of a rectangular field with a perimeter of 400 and y represents the area of the field.
y(t)=200*t-t^2 for 0<=t<400 with a sampling interval of 0.05 displaying the derivative.
We have used the view menu to set the display of the derivate on and Settings -> y-axis to set the y-axis range to -1000 <=y <=1000
From the graph we can see that the maximum value for y seems to be at t=100 and using 'Display Position' from the mode menu we can input t=100 to get the following result:
Values for 200*t-t^2:
Function: (100, 10000)
Derivative: (100, 0)
This confirms that the maximum does occur at t=100, where we have found that the derivative is 0.
The maximum area of a field of perimeter 400 is 10000 and, to obtain this area, the length of the side should be 100, i.e. the field should be a square of side 100.
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