4.3 Class Notes - Final exam Monday May 14 9-11:30 in Baker...

Final exam Monday May 14
9-11:30 in Baker 200
Announcements
Now on the course page
Final exam formula sheet - 2 pages, write on
the back of each if you want.
Practice problems and their solutions
No HWK #10. You count the best 8 out of 9,
which becomes 60/200 points on the final.
Linear approximation
0 0 0
0
1/3
( ) ( ) '( )( )
Use this fact with =512 to find an
approximation of (500)
f x f x f x x x
x
≈ + −
Solution
( )
0 0 0
1/3 2/3
0 0 0
1/3
( ) ( ) '( )( )
( ) '( ) (1/3)
1 1
=512 ( ) 8 '( )
3 64
1 1
500 8 ( 12) 8
192 16
f x f x f x x x
f x x f x x
x f x f x
−
≈ + −
= =
= = ⋅
≈ + ⋅ − = −
f(x) = x 1/3
7.8
7.9
8
8.1
8.2
475 500 525 550
Why is the curve so flat?
1/3
2/3
5/3
5
( ) (512) 8
1 1
'( ) '(512)
3 192
2 2 1
''( ) ''(512)
9 9 8
''(512) 0 c so curve is oncave
and hence lie
f x x f
f x x f
f x x f
f
−
−
= =
= =
= − = − ⋅
<
s below tangent line

Building a fence
A man is going to build a five foot tall fenced
in enclosure for his dog. One side will be
the side of his house. If he has A square
feet of fence what is the largest area he
can enclose?
y
x
Optimal fence
2
Fencing needed = 5 10 so ( 5 ) /10
5
Maximize
10
10
Derivative = 0 when /10, / 20
10
Second derivative = 1 0