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of EXERCISES 4.4 In Exercises 1-18, use the Second Derivative Test (whenever anplicable) to find the local extrema of f. Discuss concavity, ind x-coordinates of points of inflection, and sketch the graph of f. I (x) - x' - 2x + x + 1 2 f(x) x + 10x + 25x - 50 3 f(x) = 3x - 4x' + 6 4 f(x) = 8x - 2x 5 f(x) - 2x - 6x* 6 f(x) - 3x* - 5x 7 f() - (x - 1) %3D 8 f(x) = x - (16/x) 9 fx) = -1 10 f(x) - (x + 4)//

of EXERCISES 4.4 In Exercises 1-18, use the Second Derivative Test (whenever anplicable) to find the local extrema of f. Discuss concavity, ind x-coordinates of points of inflection, and sketch the graph of f. I (x) - x' - 2x + x + 1 2 f(x) x + 10x + 25x - 50 3 f(x) = 3x - 4x' + 6 4 f(x) = 8x - 2x 5 f(x) - 2x - 6x* 6 f(x) - 3x* - 5x 7 f() - (x - 1) %3D 8 f(x) = x - (16/x) 9 fx) = -1 10 f(x) - (x + 4)//

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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EXERCISES 4.4 In Exercises 1-18, use the Second Derivative Test (whenever anplicable) to find the local extrema of f. Discuss concavity, Gnd x-coordinates of points of inflection, and sketch the graph 20 f(0) - 4; (2) - 2; (5) = 6: S(0) - S(2) - 0; S'(x) > 0 if |x - I| > 1:f'(x) < 0 if x - 1| < 1: S(x) < 0 if x <l or if |x - 4| <1; S"(x) > 0 if |x - 2| <1 or if x >5. of f. 1 f(x) = x' - 2x +x + 1 21 S(0) - 2: f(2) - S(-2) = 1;f (0) = 0; S'(x) > 0 if x < 0:f'(x) < 0 if x > 0; S"(x) < 0 if |x| < 2: f"(x) > 0 if Jx > 2. 2 f(x) x' + 10x + 25x - so 3 f(x) = 3x - 4x + 6 4 f(x) - 8x - 2x* 22 S(1) - 4; f(x) > 0 if x <1: s'x) < 0 if x > 1: S"(x) > 0 for all x *1. 5 f(x) - 2x - 6x 6 f(x) = 3x - 5x 7 f(x) - (x - 1) 8 (x) - x - (16/x) 9 fx) = x- 1 10 f(x)- (x + 4)/ 11 f() = x - (27/x*) 12 f(x)-x(1-x) 13 f(x)= x/(x + 1) 23 (-2) - S(6) - -2; S(0) = f(4) = 0; f(2) = (8) = 3; Sis undefined at 2 and 6: f'(0) =1; S(x) >0 throughout (-0, 2) and (6, c): f'(x) < 0 if x - 4| < 2: f"(x) < 0 throughout (- 0o, 0), (4, 6), and (6, );f"(x) > 0 throughout (0, 2) and (2, 4). 24 S(0) - 2:f(2) - 1:f(4) = f(10) = 0; f(6) = -4;f(2) = S'(6) = 0; f'(x) <0 throughout (-0, 2), (2, 4), (4,6). and (10. o0): S'(x) > 0 throughout (6, 10); f(4) and f'(10) do not exist: f"(x) >0 throughout (-0, 2), (4, 10), and (10, c); f"(x) < 0 throughout (2, 4). %3D 14 f(x) x(x + 1) 15 ((x) = (3x + 10) 25 If n is an odd integer, then f(n) = 1 and f'(n) - 0; if n is an even integer, then f (n) = 0 and f (n) does not exist; if n is any integer then (a) f'(x) >0 whenever 2n <x< 2n + 1; (b) f'(x) <0 whenever 2n -1<x< 2n; (c) f"(x) <0 whenever 2n <x< 2n + 2. 16 f(x) = x* - 4x + 10 17 f(x) = 8x + x* 18 f(x) = x4 - In Exercises 19-26 sketch the graph of a continuous function f that satisfies all of the stated conditions. 26 f(x) = x if x= -1, 2, 4, or 8; f'(x) = 0 if x = -1, 4, 6, or 8; f'(x) < 0 throughout (-o, -1). (4, 6), and (8, 0); f'(x) > 0 throughout (-1, 4) and (6, 8); /"(x) >0 through- out (-0,0). (2, 3), and (5, 7): f"(x) <0 throughout (0, 2). (3, 5), and (7, 0). %3D 19 f(0) = 1; S(2) = 3; f(0) = f(2) = 0; s) < 0 if |x - 1| > 1: f(x) > 0 if |x - 1| < 1; (x) > 0 if x < l;f"(x) < 0 if x > 1.
Transcribed Image Text:EXERCISES 4.4 In Exercises 1-18, use the Second Derivative Test (whenever anplicable) to find the local extrema of f. Discuss concavity, Gnd x-coordinates of points of inflection, and sketch the graph 20 f(0) - 4; (2) - 2; (5) = 6: S(0) - S(2) - 0; S'(x) > 0 if |x - I| > 1:f'(x) < 0 if x - 1| < 1: S(x) < 0 if x <l or if |x - 4| <1; S"(x) > 0 if |x - 2| <1 or if x >5. of f. 1 f(x) = x' - 2x +x + 1 21 S(0) - 2: f(2) - S(-2) = 1;f (0) = 0; S'(x) > 0 if x < 0:f'(x) < 0 if x > 0; S"(x) < 0 if |x| < 2: f"(x) > 0 if Jx > 2. 2 f(x) x' + 10x + 25x - so 3 f(x) = 3x - 4x + 6 4 f(x) - 8x - 2x* 22 S(1) - 4; f(x) > 0 if x <1: s'x) < 0 if x > 1: S"(x) > 0 for all x *1. 5 f(x) - 2x - 6x 6 f(x) = 3x - 5x 7 f(x) - (x - 1) 8 (x) - x - (16/x) 9 fx) = x- 1 10 f(x)- (x + 4)/ 11 f() = x - (27/x*) 12 f(x)-x(1-x) 13 f(x)= x/(x + 1) 23 (-2) - S(6) - -2; S(0) = f(4) = 0; f(2) = (8) = 3; Sis undefined at 2 and 6: f'(0) =1; S(x) >0 throughout (-0, 2) and (6, c): f'(x) < 0 if x - 4| < 2: f"(x) < 0 throughout (- 0o, 0), (4, 6), and (6, );f"(x) > 0 throughout (0, 2) and (2, 4). 24 S(0) - 2:f(2) - 1:f(4) = f(10) = 0; f(6) = -4;f(2) = S'(6) = 0; f'(x) <0 throughout (-0, 2), (2, 4), (4,6). and (10. o0): S'(x) > 0 throughout (6, 10); f(4) and f'(10) do not exist: f"(x) >0 throughout (-0, 2), (4, 10), and (10, c); f"(x) < 0 throughout (2, 4). %3D 14 f(x) x(x + 1) 15 ((x) = (3x + 10) 25 If n is an odd integer, then f(n) = 1 and f'(n) - 0; if n is an even integer, then f (n) = 0 and f (n) does not exist; if n is any integer then (a) f'(x) >0 whenever 2n <x< 2n + 1; (b) f'(x) <0 whenever 2n -1<x< 2n; (c) f"(x) <0 whenever 2n <x< 2n + 2. 16 f(x) = x* - 4x + 10 17 f(x) = 8x + x* 18 f(x) = x4 - In Exercises 19-26 sketch the graph of a continuous function f that satisfies all of the stated conditions. 26 f(x) = x if x= -1, 2, 4, or 8; f'(x) = 0 if x = -1, 4, 6, or 8; f'(x) < 0 throughout (-o, -1). (4, 6), and (8, 0); f'(x) > 0 throughout (-1, 4) and (6, 8); /"(x) >0 through- out (-0,0). (2, 3), and (5, 7): f"(x) <0 throughout (0, 2). (3, 5), and (7, 0). %3D 19 f(0) = 1; S(2) = 3; f(0) = f(2) = 0; s) < 0 if |x - 1| > 1: f(x) > 0 if |x - 1| < 1; (x) > 0 if x < l;f"(x) < 0 if x > 1.
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