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You are here: Home / Category Index / Further Calculus And Series / Maximum Area Problems
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Maximum Area Problems - By Annie Bedford
How to use this applet:Use the textboxes to change the length and width of the rectangle. Use the change button to see the effect on the size of the rectangle. Look at the graph to see the current area's position in relation to the maximum area's position.Notes on the maths used in the applet:The maximum area can be calculated in 5 steps.
1. Derive an equation for the area of the shape.
Area = xy
2. Using the information given to you, make an equation using all the variables in the area equation and isolate one of them.
Perimeter = 24 = 2x + 2y
y = 12 - x
3. Substitute the value for the isolated term into the original area equation.
Area = x(12 - x)
Area = 12x - x2
4. Differentiate this new equation, getting a value for x and y.
12 - 2x = 0
x = 6; y = 6;
Area = 36
5. Get the second derivative to check if the value is a minimum or maximum.
-2 < 0 (maximum)
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