3.2 Class Notes - 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

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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 Max-min 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? Max-min 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 = (108-4w) w 2 Maximize (108-4w) 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 = = > <> <<
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108 w 2 -4w 3 crit. pts
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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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3.2 Class Notes - 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

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