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...

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