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

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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 00 0 0 1/3 () ( ) ' ( ) Use this fact with =512 to find an approximation of (500) fx f x x x x ≈+ Solution 0 1/3 2/3 0 ' ( ) ' () ( 1 /3 ) 11 =512 ( ) 8 '( ) 36 4 500 8 ( 12) 8 192 16 fx x f x x xf 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? 5/3 5 ( ) (512) 8 '( ) '(512) 31 9 2 22 1 ''( ) ''(512) 99 8 ''(512) 0 c so curve is oncave and hence lie f x f x f f =− =− ⋅ < s below tangent line
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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 local maximum Note that / 2.
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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).

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

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