[8] 1.
(a) Find 
if 
. Do not simplify your answer.
(b) Find 
.
(a) 
(b) 
[6] 2. Find if 
. Do not simplify your answer.
Set 
. Then 
.DIfferentiate implicitly to get 
. So 
[6] 3. Show that the function 
increases for 
.
First we find: 
. We now see that 
for . So increases for .
[5] 4. The function 
has critical points at 
and at 
. Use the second derivative test to check which of these two values yields a local minimum.
;
Since 
we have a local maximum for at the point .
Since 
we have a local minimum for at the point .