Optimization Problems in Calculus

Optimization Problems in Calculus

Assessment

Interactive Video

Mathematics

9th - 10th Grade

Practice Problem

Easy

Created by

Thomas White

Used 1+ times

FREE Resource

The video tutorial explores optimization problems using calculus, starting with a real-life example of maximizing the area of a rectangle formed from a wire. It then presents a problem involving Alex, who must find the fastest route to an island by optimizing his running and swimming distances. The tutorial explains how to use derivatives to find the minimum travel time, demonstrating the power of calculus in solving practical problems.

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16 questions

Show all answers

1.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the primary focus of optimization problems?

Using algebraic equations

Guessing the best solution

Using calculus to find exact solutions

Trial and error

2.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

In the wire problem, what is the goal?

To find the longest rectangle

To find the smallest square

To find the rectangle with minimum perimeter

To find the rectangle with maximum area

3.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the length of the wire used in the rectangle problem?

75 meters

100 meters

50 meters

150 meters

4.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the area of a square formed from the wire?

525 square units

700 square units

400 square units

625 square units

5.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the distance Alex's cabin is from the closest point on the beach?

8 km

6 km

4 km

2 km

6.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is Alex's running speed along the beach?

3 km/h

5 km/h

8 km/h

10 km/h

7.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the main objective in Alex's travel problem?

Maximize the distance traveled

Minimize the travel time

Minimize the running distance

Maximize the swimming distance

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