# Solution

## Solution

﻿Solutions to the Assignment #3
1)

Note:
2)

3)

Note:
4)

Note:
5)

Note:
6)
Let then
Let then

7)

Note:
8)

Note:
9)

Divide both sides by 2

Solve for by subtracting both sides by then dividing both sides by

10)

; Note: apply the product rule to the term:

Solve for by subtracting both sides by and adding y then dividing both sides by

11)

Solve for by multipling both sides by then substituting

12)
Let

Apply the product rule to

Multiply both sides by

Substitute

13)

14)

15)

Apply the product rule to

Simplify the term by using as a common denominator

16)

17) Intervals on which then increases/rises on those intervals.
Intervals on which then decreases/falls on those intervals.
falls on intervals and so on these intervals.
rises on interval so on this interval.
18) falls on intervals and so on these intervals.
19) To find critical values of by finding all real values that make or undefined.

Setting then solve for real solutions

Dividing both sides by 12

or
or
There are two critical values.
20)

Setting then solve for real solutions.

Using the quadratic formula with , , and

and are the critical values
21)
Find the critical values of by solving for real solutions.

Solve for real solutions.
Dividing both sides by 3

or
The two critical values -4 and 2 dividing the real line into three intervals
), ,
Interval
Test value

)
-5

0

3

increases on
decreases on
22)
Find the critical values of by solving for real solutions.

Solve for real solutions.
Dividing both sides by 3

or
The two critical values -12 and 0 dividing the real line into three intervals
), ,
Interval
Test value

)
-13

-1

1

increases on
decreases on
23)
Find...