Skip to content Skip to navigation

Connexions

You are here: Home » Content » Optimization of a Function (Student Page)

Navigation

Recently Viewed

This feature requires Javascript to be enabled.
 

Optimization of a Function (Student Page)

Module by: Debbie Trahan. E-mail the author

Summary: This is the student page for the Optimization of a Function Module. The student will write and graph linear functions then use these functions to write a new function using the Pythagorean Theorem. The students will then find the minimum value of the new function using a graphing calculator.

Lesson Objective

During this lesson, you will review linear functions and the Pythagorean Theorem. You will use these topics to help you write a new function then find the minimum value of the new function.

Problem

Ship A is 360 kilometers east of Shipwreck Island traveling due west toward Shipwreck Island at a speed of 15 kilometers per hour (km/hr). Ship B is 45 kilometers north of Shipwreck Island traveling due north away from Shipwreck Island at a speed of 10 km/hr. (see figure 1)

Figure 1
Figure 1 (optfig1.png)

a

Let Shipwreck Island be at the origin.

Write a function for Ship A’s distance from Shipwreck Island in terms of the time t t .

Write a function for Ship B’s distance from Shipwreck Island in terms of the time t t .

Graph the functions on the coordinate plane shown in Figure 2.

Figure 2
Figure 2 (optfig2.jpg)

b

Find the distance, in kilometers, between Ship A and Ship B after 10 hours.

c

Find the location of Ship B when Ship A is 120 miles from Shipwreck Island.

d

At what time are the ships the same distance from Shipwreck Island?

e

Find the distance for Ship B when Ship A reaches Shipwreck Island.

f

Write a function for the distance between Ship A and Ship B in terms of the time.

g

Graph the function that you wrote in part f on a graphing calculator. Use a calculator to help you approximate when the distance between Ship A and Ship B is the least. Approximate the distance at this time.

Answers

When you are have completed the questions in this lesson, click on the answer key below to view the answers.

Go to Answers

Content actions

Download module as:

PDF | EPUB (?)

What is an EPUB file?

EPUB is an electronic book format that can be read on a variety of mobile devices.

Downloading to a reading device

For detailed instructions on how to download this content's EPUB to your specific device, click the "(?)" link.

| More downloads ...

Add module to:

My Favorites (?)

'My Favorites' is a special kind of lens which you can use to bookmark modules and collections. 'My Favorites' can only be seen by you, and collections saved in 'My Favorites' can remember the last module you were on. You need an account to use 'My Favorites'.

| A lens I own (?)

Definition of a lens

Lenses

A lens is a custom view of the content in the repository. You can think of it as a fancy kind of list that will let you see content through the eyes of organizations and people you trust.

What is in a lens?

Lens makers point to materials (modules and collections), creating a guide that includes their own comments and descriptive tags about the content.

Who can create a lens?

Any individual member, a community, or a respected organization.

What are tags? tag icon

Tags are descriptors added by lens makers to help label content, attaching a vocabulary that is meaningful in the context of the lens.

| External bookmarks