Exercises

Use Maple commands to optimize following expressions.

Type each Maple command instead of using the context sensitive menus.

1. Find the minimum: ${(2x-3)}^2+2x$

           expr1:=(2*x-3)^2 → + 2*x
           plot(expr1, x=-10..10)
           deriv := diff(expr1, x)
           minx := solve(deriv=0, x)
           minval := subs(x=minx,expr1)

2. Find all local and absolute minima and maxima: $x^4-3x^2+x$

   

   Look at the plot and decide which roots will produce the local maximums and minimums and the absolute minimum. Be sure to sub back into the expression to find the actual max or min value.

3. Find maximum: $\frac{7}{3}-\frac{1}{3}{\left(3x-\frac{5}{2}\right)}^2$

               expr3:= 7/3 → -1/3 → * (3*x-5/2)^2
               plot(expr3, x=-4..4, y=-50..10)
               dexpr3 := diff(expr3, x)
               maxX := solve(dexpr3=0, x)
               maxVal := subs(x=maxX, expr3)
             

Use the Right Click Menu

1. Minimum: ${(2x-3)}^2+2x$

            (2x-3)^2 → + 2x
            (Right-click:Plots -> 2-D Plot)
            (Right-click expression: Differentiate -> x)
            (Right-click result: solve)