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Steps
Formulas (2D)
Formulas (3D)
Primary Equation
Secondary Equation
100
Determine the desired maximum or minimum value by deriving and setting the equation equal to zero.
What is step 5?
100
(1/2)bh
What is the area of a triangle?
100
s^3
What is the volume of a cube?
100
Fence has given perimeter of 100m and needs a max area.
What is l*w?
100
A cage is being built to be 300ft^3. It has dimensions to minimize the amount of cage used.
What is 300=l*w*h?
200
Identify all given quantities to be determined and possibly make a sketch.
What is step 1?
200
pi*r^2
What is the area of a circle?
200
pi*r^2*h
What is the volume of a cylinder?
200
A fence with one end open to a river must contain 200ft^2 of land and perimeter needs to be minimized
What is 2l+w?
200
A rectangle has a perimiter of 400in and has a maximum area
What is 400=2l+2w?
300
Determine the feasable domain of the primary equation. e.g. Figure out what values will make the problem make sense.
What is step 4?
300
a^2 + b^2 = c^2
What is the Pythagorean Theorem?
300
(4/3)*pi*r^2
What is the volume of a sphere?
300
A box has a fixed surface area of 30in and volume needs to be maximized
What is l*w*h?
300
A house is being built with a dirt floor and a flat roof. It has a surface area of 100ft and its area is maximized.
What is 1000=4s+r?
400
Write a primary equation for the quantity being optimized.
What is step 2?
400
(1/2)(b1+b2)h
What is the area of a trapezoid?
400
(pi*r^2*h)/3
What is the volume of a cone?
400
A window is constructed to have a semicircle built atop a rectangle. It has maximum area and a perimeter of 16 ft.
What is x*y*pi*(x/2)^2
400
A rectangle is inside the semicircle sqrt(25-x^2). It has dimensions that give it a maximum area.
What is no secondary equation? :p
500
Reduce the primary equation to having one independant variable. This may involve the use of a secondary equation.
What is step 2?
500
(theta*r^2)/2
What is the area of a sector of a circle?
500
(1/3)l*w*h
What is the volume of a pyramid?
500
A rectangle is bounded by the x- and y- axis on the graph of y=(6-x)/2. It has a legnth that maximizes its area.
What is (6x-x^2)/2
500
a rectangle has mazimum area and is inscribed by the ellipse given by (x^2)/144+(y^2)/16=1
What is x=sqrt(144-9y^2)?