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Unformatted text preview: Section 4.1
39. 42. 131 [ 2.35, 2.35] by [ 3.5, 3.5] [ 4, 4] by [ 1, 6] y x
x
2 1 2 4 (4 4 x2
2 x2 x) ( 2x)
4 4 (1) 4
2x 2 x2 x2 y 1, 2 2x, x x 0 0 extremum value local min local max 3 4 crit. pt. derivative x x 0 1 undefined 0 crit. pt. x x x x 40. 2 2 2 2 derivative extremum value undefined local max 0 0 minimum maximum 0 2 2 0 y
[ 4, 6] by [ 2, 6] 43. undefined local min 2x 2x 2, 6, x x 1 1 crit. pt. derivative extremum value x
[ 4.7, 4.7] by [ 1, 5] 1 1 3 0 0 maximum maximum 5 1 5 x x 2x
5x
2 undefined local min y x2
x
2 1 2 3 4x(3 3 x x ( 1)
x) 3
12x x x 44. 2 2 3 crit. pt. x x x 41. 0
12 5 derivative extremum 0 0 minimum local max value 0
144 1/2 15 125 [ 4, 6] by [ 5, 5] 4.462 We begin by determining whether f (x) is defined at x where f (x)
1 2 x 4 1 x 2 15 , 4 1, 3 undefined minimum 0 x x 1 1 x3 6x 2 8x, Lefthand derivative: lim
h0 f (1 h) h f (1) lim
h0 1 (1 4 h)2 1 (1 2 h) 15 4 3 [ 4.7, 4.7] by [0, 6.2] lim
h0 y 2, 1, x x 1 1 extremum value minimum 2 h2 h 4h 1 ( h 4 h lim
h0 4h) crit. pt. derivative x 1 undefined 1 Righthand derivative: lim
h0 f (1 lim
h0 h) f (1) h (1 h)3 h3 3h 2 h 6(1 h h)2 h 8(1 h) 3 lim
h0 h0 lim (h 2 1 Thus f (x) 3h
1 x 2 1)
1 , 2 x 8, x 1 1 3x 2 12x ...
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This note was uploaded on 10/05/2011 for the course MAC 1147 taught by Professor German during the Fall '08 term at University of Florida.
 Fall '08
 GERMAN
 Derivative

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