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6. Determine the point of inflection on the curve defined by y=x³ + 5. Show that the tangent line at this point crosses the curve. 7. Sketch a graph of

6. Determine the point of inflection on the curve defined by y=x³ + 5. Show that the tangent line at this point crosses the curve. 7. Sketch a graph of

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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#6 and #8 please
5. For each of the following, check for discontinuities and state the equation of any vertical asymptotes. Conduct a limit test to determine the behaviour of the curve on either side of the asymptote. a. y = 2x x-3 c. f(x) = x² - 2x - 15 x+3 5 x-5 b. g(x) = x+5 d. g(x) = 1² -x-20 6. Determine the point of inflection on the curve defined by y = x³ + 5. Show that the tangent line at this point crosses the curve. 7. Sketch a graph of a function that is differentiable on the interval -3 ≤ x ≤ 5 and satisfies the following conditions: . There are local maxima at (-2, 10) and (3, 4). ● The function fis decreasing on the intervals -2<x< 1 and 3 ≤ x ≤ 5. ● The derivative f'(x) is positive for -3 = x < -2 and for 1 < x < 3. . • f(1) = -6 8. Each of the following graphs represents the second derivative, g"(x), of a function g(x): a. b. ↑8"(x) ↑8"(x) X -210 i 2 3 4-20 12 6 g"(x) is a quadratic function. g"(x) is a cubic function. i. On what intervals is the graph of g(x) concave up? On what intervals is the graph concave down? ii. List the x-coordinates of the points of inflection. iii. Make a rough sketch of a possible graph for g(x), assuming that g(0) = -3. CHAPTER 4 217
Transcribed Image Text:5. For each of the following, check for discontinuities and state the equation of any vertical asymptotes. Conduct a limit test to determine the behaviour of the curve on either side of the asymptote. a. y = 2x x-3 c. f(x) = x² - 2x - 15 x+3 5 x-5 b. g(x) = x+5 d. g(x) = 1² -x-20 6. Determine the point of inflection on the curve defined by y = x³ + 5. Show that the tangent line at this point crosses the curve. 7. Sketch a graph of a function that is differentiable on the interval -3 ≤ x ≤ 5 and satisfies the following conditions: . There are local maxima at (-2, 10) and (3, 4). ● The function fis decreasing on the intervals -2<x< 1 and 3 ≤ x ≤ 5. ● The derivative f'(x) is positive for -3 = x < -2 and for 1 < x < 3. . • f(1) = -6 8. Each of the following graphs represents the second derivative, g"(x), of a function g(x): a. b. ↑8"(x) ↑8"(x) X -210 i 2 3 4-20 12 6 g"(x) is a quadratic function. g"(x) is a cubic function. i. On what intervals is the graph of g(x) concave up? On what intervals is the graph concave down? ii. List the x-coordinates of the points of inflection. iii. Make a rough sketch of a possible graph for g(x), assuming that g(0) = -3. CHAPTER 4 217
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