Homework 12
Math 1100
Name:
30 September, 2013
1I
1. Let f(x)=x
2x
3
(a) (4 points) Find
f’(x).
(b) (4 points) Find
f”(x).
.1’(x c,x
f.
(c) (4 points) Find all critical values of
—ZQ
1
x
3
3i 2.
y
27
(d) (4 points) On what intervals is
I
f(x)
concave up?
f
>
H()
(i)
v1
50
(e) (4 points) On what intervals is
(.or’
(-00,0)
,
f(x)
concave down?
So
(x)
,s
coy1cc
(f) (4 points) Find all relative maximum points of f(x). Give the point, not just the
-value. Justify your answer with reference to the second derivative and/or the
concavity of the function.
c “(-r)
X:
‘-
3J
‘%
-
-
_
3
1
L’
r3j 2I--l
o)
(-
‘33
j3
(g) (4 points) Find all relative minimum points of f(x). Give the point, not just the
rvalue. Justify your answer with reference to the second derivative and/or the
concavity of the function.
5
rrTz
+
(-7’ç
I
f-Co Ias
-
Hi
t;
21z..
-
(.‘—1.9)
(h) (4 points) Draw the graph of
f(x)
on the axes below.
IMI)111,)1WI
x=. /::