A cardboard box manufacturer wishes to make open boxes from rectangular pieces of cardboard with dimensions 16cm by 30cm by cutting equal squares from the four corners and turning up the sides. State the formula for the volume of a rectangular prism (aka box). Express the volume formula as a function of x. What is the domain of V?
A cardboard box manufacturer wishes to make open boxes from rectangular pieces of cardboard with dimensions 16cm by 30cm by cutting equal squares from the four corners and turning up the sides. State the formula for the volume of a rectangular prism (aka box). Express the volume formula as a function of x. What is the domain of V?
Chapter3: Polynomial Functions
Section3.5: Mathematical Modeling And Variation
Problem 7ECP: The kinetic energy E of an object varies jointly with the object’s mass m and the square of the...
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A cardboard box manufacturer wishes to make open boxes from rectangular pieces of cardboard with dimensions 16cm by 30cm by cutting equal squares from the four corners and turning up the sides.
- State the formula for the volume of a rectangular prism (aka box).
- Express the volume formula as a function of x.
- What is the domain of V?
- Find the derivative of V(x) with respect to x.
- Find the function values at the critical number/s and at the endpoints.
- What is the largest possible volume of the box?
- What is the length of the side of the cut-out square that will make the box which has the largest possible volume?
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