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?

As per bartleby guidelines we only give first three question answers.

Answered: A cardboard box manufacturer wishes to…

College Algebra (MindTap Course List)

12th Edition

ISBN:9781305652231

Author:R. David Gustafson, Jeff Hughes

Publisher:R. David Gustafson, Jeff Hughes

Chapter3: Functions

Section3.3: More On Functions; Piecewise-defined Functions

Problem 99E: Determine if the statemment is true or false. If the statement is false, then correct it and make it...

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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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