Math

MA 141 Homework 4.1

Pitts SHOW YOUR WORK! Name _______________________

1. (See # 20) Find the interval(s) where the function 3

( ) 3 4f x x x   is increasing and the interval(s)

where it is decreasing. Show your calculus to justify your answer. Show your sign graph clearly

In interval notation: increasing over ______________________ decreasing over ______________________

2. (See # 28) Find the interval(s) where the function 2

2 ( )

1

t g t

t 

 is increasing and the interval(s) where it

is decreasing. Show your calculus to justify your answer. Show your sign graph clearly

In interval notation: increasing over ______________________ decreasing over ______________________

3. (See # 36) Showing your calculus, find the interval(s) where the function 2

( ) 1

x g x

x 

 is increasing and the

interval(s) where it is decreasing. Show your sign graph clearly.

In interval notation: increasing over ______________________ decreasing over ______________________

4. (See # 60) Showing your calculus, find the relative maxima and relative minima, if any, of the

function 5 3

( ) 3 20 20F t t t   . Justify your answer.

5. (See # 68) Showing your calculus, find the relative maxima and relative minima, if any, of the

function 2

( ) 1

x g x

x 

 . Justify your answer.

6. (See 4.1 # 72) The Mexican subsidiary of ThermoMaster manufactures an indoor-outdoor thermometer. Management estimates that the profit (in dollars) realizable by the company for manufacture and sale of x units of

thermometers each week is 2

( ) 0.001 8 5000P x x x    . Showing your calculus, find the interval(s) where

the profit function P is increasing and the interval(s) where P is decreasing?

7. (See 4.1 # 78) The average cost (in dollars) incurred by Lincoln Records each week in pressing x compact discs

is given by 2000

( ) 0.0001 2 (0 6000)C x x x x

      Showing your calculus, Show that ( )C x is

decreasing over the interval (0, 6000).