Unit 5

Applications of Derivatives

A. Maximum and Minimum Problems

Lesson 2: Extreme Values of Distance and Time and Economics

Extreme Values of Distance and Time

Suppose an airplane flying west at «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mn»200«/mn»«mo»§#160;«/mo»«mi»km«/mi»«/math» passes over a house «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mn»10«/mn»«/math» minutes before another plane, flying south at «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mn»300«/mn»«mo»§#160;«/mo»«mi»km«/mi»«mo»/«/mo»«mi mathvariant=¨normal¨»h«/mi»«/math», passes over the same house. The planes are at the same altitude.

Imagine what this scenario looks like and think about when you would expect the two planes to be closest together.

Compare your thoughts with the simulation in the following applet.

Interactive

Click the interactive button to open the applet Minimum Distance. To use the applet, drag the blue button to see the planes move as the time changes.

Can you think of a function that describes the distance between the planes over time?