example 3 Average Cost

Chapter 6.5

225 13( )

x xC x

x

a. Graph the function on the window [-20, 20] by [-30, 50].

b. Does the graph in (a) have a horizontal asymptote?

c. Graph the function on the window [0, 20] by [0, 50].

d. Does the graph of the function using the window in part (a) or part (b) better model the average cost function? Why?

e. Use technology to find the minimum average cost and the number of units that gives the minimum average cost.

The function represents the daily average cost (in $hundreds) for the

production of Stanley golf carts, with x equal to the number of golf carts produced.

2009 PBLPathways

2009 PBLPathways

225 13( )

x xC x

x

a. Graph the function on the window [-20, 20] by [-30, 50].

b. Does the graph in (a) have a horizontal asymptote?

c. Graph the function on the window [0, 20] by [0, 50].

d. Does the graph of the function using the window in part (a) or part (b) better model the average cost function? Why?

e. Use technology to find the minimum average cost and the number of units that gives the minimum average cost.

The function represents the daily average cost (in $hundreds) for the

production of Stanley golf carts, with x equal to the number of golf carts produced.

2009 PBLPathways

225 13( )

x xC x

x

a. Graph the function on the window [-20, 20] by [-30, 50].

x

x

( )C x ( )C x

The function represents the daily average cost (in $hundreds) for the

production of Stanley golf carts, with x equal to the number of golf carts produced.

2009 PBLPathways

225 13( )

x xC x

x

x

x

( )C x ( )C x

a. Graph the function on the window [-20, 20] by [-30, 50].

The function represents the daily average cost (in $hundreds) for the

production of Stanley golf carts, with x equal to the number of golf carts produced.

2009 PBLPathways

225 13( )

x xC x

x

x

x

( )C x ( )C x

b. Does the graph in (a) have a horizontal asymptote?

The function represents the daily average cost (in $hundreds) for the

production of Stanley golf carts, with x equal to the number of golf carts produced.

2009 PBLPathways

225 13( )

x xC x

x

x

x

( )C x ( )C x

b. Does the graph in (a) have a horizontal asymptote?

225 13( )

x xC x

x

Degree of numerator is 2

Degree of denominator is 1

The function represents the daily average cost (in $hundreds) for the

production of Stanley golf carts, with x equal to the number of golf carts produced.

2009 PBLPathways

225 13( )

x xC x

x

c. Graph the function on the window [0, 20] by [0, 50].

x

x

( )C x ( )C x

The function represents the daily average cost (in $hundreds) for the

production of Stanley golf carts, with x equal to the number of golf carts produced.

2009 PBLPathways

225 13( )

x xC x

x

d. Does the graph of the function using the window in part (a) or part (b) better model the average cost function? Why?

x

x

( )C x ( )C x

The function represents the daily average cost (in $hundreds) for the

production of Stanley golf carts, with x equal to the number of golf carts produced.

2009 PBLPathways

225 13( )

x xC x

x

d. Does the graph of the function using the window in part (a) or part (b) better model the average cost function? Why?

x

x

( )C x ( )C x

The function represents the daily average cost (in $hundreds) for the

production of Stanley golf carts, with x equal to the number of golf carts produced.

2009 PBLPathways

225 13( )

x xC x

x

e. Use technology to find the minimum average cost and the number of units that gives the minimum average cost.

x

x

( )C x ( )C x

The function represents the daily average cost (in $hundreds) for the

production of Stanley golf carts, with x equal to the number of golf carts produced.

2009 PBLPathways

225 13( )

x xC x

x

e. Use technology to find the minimum average cost and the number of units that gives the minimum average cost.

x

x

( )C x ( )C x

(5, 23)

The function represents the daily average cost (in $hundreds) for the

production of Stanley golf carts, with x equal to the number of golf carts produced.

2009 PBLPathways

225 13( )

x xC x

x

e. Use technology to find the minimum average cost and the number of units that gives the minimum average cost.

x

x

( )C x ( )C x

(5, 23)

5 golf carts produced

minimizes

daily average cost at $2300 per cart

The function represents the daily average cost (in $hundreds) for the

production of Stanley golf carts, with x equal to the number of golf carts produced.