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Note for MATH 1330 at UH 2

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This 3 page Class Notes was uploaded by an elite notetaker on Friday February 6, 2015. The Class Notes belongs to a course at University of Houston taught by a professor in Fall. Since its upload, it has received 12 views.

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Date Created: 02/06/15
Math 1330 Section 24 Applications and Writing Functions We can use techniques from this chapter to solve problems First however we have to write functions from a description of a situation Here are some hints for writing functions 0 Read the problem carefully What are you trying to nd Write down the speci c function you need 0 Draw a picture of the situation if you can Label your picture with appropriate variables 0 If you can t draw a picture assign variables to the quantities mentioned in the problem 0 If the problem mentions a formula e g perimeter area volume distance write it down Ifnot try to write an equation that relates the problems mentioned in the problem 0 If necessary solve your formula or equation to get the function you need You may need to write two equations and then use substitution to get the required function For applications involving quadratic functions you can use the vertex to answer most questions Use jf 1 whenever possible 2a 2a Example 1 The perimeter of a rectangle is 78 inches a Express its area A as a function of its width w b For what value of w is the area the greatest c What is the maximum area of the rectangle Example 2 The sum of two numbers is 24 Find the smallest possible value of the sum of their squares Example 3 A farmer has 1800 feet of fencing He wants to use it to fence in a rectangular field that borders along the straight edge of a river No fencing will be needed along the river What are the dimensions of the field that has the largest area that he can fence in using the fencing Example 4 A rectangle has a base on the x axis and its upper two vertices are on the parabola y 25 x2 a Express the area A of the rectangle as a function of x b Express the perimeter P of the rectangle as a function of x Example 5 An opentop box with a square base has volume 24 cubic cm Express the surface area S of the box as a function ofx where x is the length ofa side ofthe base of the box Example 6 A wire of length x is bent into the shape of a rectangle whose length is three times its width a Express the area A of the rectangle as a function of x b Express the length of the diagonal d as a function of x Example 7 Suppose Pxyis a point on the graph of the function fx x2 5 Express the distance d from P to the point 0 3

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