This preview shows pages 1–3. Sign up to view the full content.
Problem
(a) Find all the critical points (x values),
(b) Use the second derivative test to
determine if they are local max or min
Find the open intervals on which the function
is (c) increasing, (d) convex
42
()
8
fx
x
x
=−
Solution
32
22
8
'( )
4
16
4 (
4)
4(
2) (
2)
''( )
12
0
convex when
4 / 3
crit. pts
 2
2
min
max
increasing
2
0,
2
fx x
x
x
x xx
x
x
xx
=−=
−
+
>
>
↓↑
↓
↑
−<<
>
f(x) = x
4
–8x
2
crit. pts.
2,0,2
20
10
0
10
20
30
40
50
60
3.5
3
2.5
2
1.5
1
0.5
0
0.5
1
1.5
2
2.5
3
3.5
Maxmin word problem
A parcel delivery service will only deliver a
package if its length plus its girth (2w+2h)
is less than 108 inches. What is the box of
largest volume with w=h that they will
deliver?
Maxmin word problem
A parcel delivery service will only deliver a
package if its length plus its girth (2w+2h)
is less than 108 inches. What is the box of
largest volume with w=h that they will
deliver?
108 = L + 2w + 2h = L + 4w
Maximize
Lwh = (1084w) w
2
Maximize
(1084w) w
2
L = 108  4w
23
2
() 1
0
8
4
'( )
216
12
0
when
0,18
''( )
216
24
convex
when
9
''(18)
0
max
''(0)
216
min
12 (18
)
0
18
increasing
0
18
Vw
w
w
w
w
w
w
w
VV
w
w
w
=
=
>
<>
↓
<<
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document 108
w
2
4w
3
crit. pts
This is the end of the preview. Sign up
to
access the rest of the document.
This note was uploaded on 11/14/2007 for the course MATH 1106 taught by Professor Durrett during the Spring '07 term at Cornell University (Engineering School).
 Spring '07
 DURRETT
 Calculus, Critical Point, Derivative

Click to edit the document details