Calculus and Geometry Concepts

Calculus and Geometry Concepts

Assessment

Interactive Video

Mathematics

9th - 10th Grade

Practice Problem

Hard

Created by

Thomas White

FREE Resource

The video tutorial explains how to find the dimensions of a rectangle with a fixed area of 1,000 square meters that minimizes the perimeter. It involves setting up constraint and objective equations, solving for variables, and using calculus to find the minimum perimeter. The solution reveals that the rectangle is actually a square, confirmed by the second derivative test.

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11 questions

Show all answers

1.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the primary goal when finding the dimensions of the rectangle in this problem?

Maximize the perimeter

Minimize the area

Minimize the perimeter

Maximize the area

2.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What are the labels used for the horizontal and vertical sides of the rectangle?

M and N

X and Y

L and W

A and B

3.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the constraint equation based on?

The width of the rectangle

The length of the rectangle

The area of the rectangle

The perimeter of the rectangle

4.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the formula for the perimeter of a rectangle?

Length + Width

2 * Length + Width

2 * Length + 2 * Width

Length + 2 * Width

5.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Which variable is traditionally solved for in the constraint equation?

W

Z

Y

X

6.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the purpose of substituting the constraint equation into the objective equation?

To simplify the constraint equation

To find the maximum perimeter

To express the objective equation in terms of a single variable

To eliminate the variable Y

7.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Why is the objective equation rewritten before differentiation?

To make it more complex

To make differentiation easier

To change the variable

To eliminate constants

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