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g(x)=x-bx³ +a+c. Use calculus to: St (a) Find the critical points of g(x). (Round the y-value to 3 decimal places, where appropriate) (b) Create a table of signs for g(x). (c) Find the intervals where g(x) is increasing or decreasing, using interval notation. (d) Find any local minima and maxima of g(x). (e) Find the intervals (using interval notation) where g(x) is concave up and concave down, and any points of inflections. (f) Use the information from parts (a)-(e) to sketch a graph of g(x), including all relevant information. (You can use technology) Note: (Show detailed working or explain your answer. Unsupported answers will not receive marks.) 5. Let

g(x)=x-bx³ +a+c. Use calculus to: St (a) Find the critical points of g(x). (Round the y-value to 3 decimal places, where appropriate) (b) Create a table of signs for g(x). (c) Find the intervals where g(x) is increasing or decreasing, using interval notation. (d) Find any local minima and maxima of g(x). (e) Find the intervals (using interval notation) where g(x) is concave up and concave down, and any points of inflections. (f) Use the information from parts (a)-(e) to sketch a graph of g(x), including all relevant information. (You can use technology) Note: (Show detailed working or explain your answer. Unsupported answers will not receive marks.) 5. Let

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter4: Polynomial And Rational Functions
Section: Chapter Questions
Problem 15T
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Solve the part d, e and f I attached the answers of part a , b and c
g(x)=x5-bx³+a+c. Use calculus to: st (a) Find the critical points of g(x). (Round the y-value to 3 decimal places, where appropriate) (b) Create a table of signs for g(x). (c) Find the intervals where g(x) is increasing or decreasing, using interval notation. (d) Find any local minima and maxima of g(x). (e) Find the intervals (using interval notation) where g(x) is concave up and concave down, and any points of inflections. (f) Use the information from parts (a)-(e) to sketch a graph of g(x), including all relevant information. (You can use technology) Note: (Show detailed working or explain your answer. Unsupported answers will not receive marks.) 5. Let
Transcribed Image Text:g(x)=x5-bx³+a+c. Use calculus to: st (a) Find the critical points of g(x). (Round the y-value to 3 decimal places, where appropriate) (b) Create a table of signs for g(x). (c) Find the intervals where g(x) is increasing or decreasing, using interval notation. (d) Find any local minima and maxima of g(x). (e) Find the intervals (using interval notation) where g(x) is concave up and concave down, and any points of inflections. (f) Use the information from parts (a)-(e) to sketch a graph of g(x), including all relevant information. (You can use technology) Note: (Show detailed working or explain your answer. Unsupported answers will not receive marks.) 5. Let
g(x) = x5-12x³ +15+15 = g'(x) = d(x5-12x³ +30) = dx 2 ⇒ g'(x) = x² ( 5x²-36) __for critical point pul g'(x) = 0 X = 0 Sign scheme of at x = 0 g(0) = 30 6 55 07 at x = ·at x = G 15 a) Critical point of g(x) (0,0); (5) " by Sign scheme of g'(x) 2 g'(x) = ( x + ( tve ⇒ x² ( 5x²-36) = 0 CY x = 1 F → 9( † / ) = 62.7342 → 9(-) = 122.734 - 62.7342); √5 ਨ ) (X - — // ) .ve tve √5 (5,0) 1 -0 Increasing: Decreasing: - 55 x-) 5 -ve 0 " x512x³ +30 5x4-36x2 √5 ); F) " 122.734)
Transcribed Image Text:g(x) = x5-12x³ +15+15 = g'(x) = d(x5-12x³ +30) = dx 2 ⇒ g'(x) = x² ( 5x²-36) __for critical point pul g'(x) = 0 X = 0 Sign scheme of at x = 0 g(0) = 30 6 55 07 at x = ·at x = G 15 a) Critical point of g(x) (0,0); (5) " by Sign scheme of g'(x) 2 g'(x) = ( x + ( tve ⇒ x² ( 5x²-36) = 0 CY x = 1 F → 9( † / ) = 62.7342 → 9(-) = 122.734 - 62.7342); √5 ਨ ) (X - — // ) .ve tve √5 (5,0) 1 -0 Increasing: Decreasing: - 55 x-) 5 -ve 0 " x512x³ +30 5x4-36x2 √5 ); F) " 122.734)
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