Pre-Calc Homework Solutions 130

Pre-Calc Homework Solutions 130 - (c) No, since the left-...

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30. [ 2 5, 5] by [ 2 0.8, 0.6] Maximum value is } 1 2 } at x 5 0; minimum value is 2} 1 2 } at x 52 2. 31. [ 2 6, 6] by [0, 12] Maximum value is 11 at x 5 5; minimum value is 5 on the interval [ 2 3, 2]; local maximum at ( 2 5, 9) 32. [ 2 3, 8] by [ 2 5, 5] Maximum value is 4 on the interval [5, 7]; minimum value is 2 4 on the interval [ 2 2, 1]. 33. [ 2 6, 6] by [ 2 6, 6] Maximum value is 5 on the interval [3, ); minimum value is 2 5 on the interval ( 2‘ , 2 2]. 34. [ 2 6, 6] by [0, 9] Minimum value is 4 on the interval [ 2 1, 3] 35. (a) No, since f 9 ( x ) 5 } 2 3 } ( x 2 2) 2 1/3 , which is undefined at x 5 2. (b) The derivative is defined and nonzero for all x ± 2. Also, f (2) 5 0 and f ( x ) . 0 for all x ± 2. (c) No, f ( x ) need not not have a global maximum because its domain is all real numbers. Any restriction of f to a closed interval of the form [ a , b ] would have both a maximum value and a minimum value on the interval. (d) The answers are the same as (a) and (b) with 2 replaced by a . 36. Note that f ( x ) 5 h Therefore, f 9 ( x ) 5 h (a) No, since the left- and right-hand derivatives at x 5 0 are 2 9 and 9, respectively. (b) No, since the left- and right-hand derivatives at x 5 3 are 2 18 and 18, respectively.
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Unformatted text preview: (c) No, since the left- and right-hand derivatives at x 5 2 3 are 2 18 and 18, respectively. (d) The critical points occur when f 9 ( x ) 5 0 (at x 5 6 3 w ) and when f 9 ( x ) is undefined (at x 5 0 or x 5 6 3). The minimum value is 0 at x 5 2 3, at x 5 0, and at x 5 3; local maxima occur at ( 2 3 w , 6 3 w ) and ( 3 w , 6 3 w ). 37. [ 2 4, 4] by [ 2 3, 3] y 9 5 x 2/3 (1) 1 } 2 3 } x 2 1/3 ( x 1 2) 5 } 5 3 x 1 3 x w 4 } 38. [ 2 4, 4] by [ 2 3, 3] y 9 5 x 2/3 (2 x ) 1 } 2 3 } x 2 1/3 ( x 2 2 4) 5 } 8 x 3 2 3 2 x w 8 } x , 2 3 or 0 , x , 3 2 3 , x , 0 or x . 3. 2 3 x 2 1 9, 3 x 2 2 9, x # 2 3 or 0 # x , 3 2 3 , x , 0 or x $ 3. 2 x 3 1 9 x , x 3 2 9 x , 130 Section 4.1 crit. pt. derivative extremum value x 5 2 1 minimum 2 3 x 5 undefined local max x 5 1 minimum 2 3 crit. pt. derivative extremum value x 5 2} 4 5 } local max } 1 2 2 5 } 10 1/3 < 1.034 x 5 undefined local min...
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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.

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