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You use 'INF' for ∞o and And use 'U' for the union symbol. Enter DNE if an answer does not exist. for f(x) = x³ +4.5x² - 12x - 2 a) Determine the intervals on which f is concave up and concave down. f is concave up on: 9- f is concave down on: b) Based on your answer to part (a), determine the inflection points of f. Each point should be entered as an ordered pair (that is, in the form (x, y)). (Separate multiple answers by commas.) c) Find the critical numbers of f and use the Second Derivative Test, when possible, to determine the relative extrema. List only the x-coordinates. Relative maxima at: Relative minima at: (Separate multiple answers by commas.) (Separate multiple answers by commas.) d) Find the x-value(s) where f'(x) has a relative maximum or minimum. f' has relative maxima at: f' has relative minima at: (Separate multiple answers by commas.) (Separate multiple answers by commas.) Instruction

You use 'INF' for ∞o and And use 'U' for the union symbol. Enter DNE if an answer does not exist. for f(x) = x³ +4.5x² - 12x - 2 a) Determine the intervals on which f is concave up and concave down. f is concave up on: 9- f is concave down on: b) Based on your answer to part (a), determine the inflection points of f. Each point should be entered as an ordered pair (that is, in the form (x, y)). (Separate multiple answers by commas.) c) Find the critical numbers of f and use the Second Derivative Test, when possible, to determine the relative extrema. List only the x-coordinates. Relative maxima at: Relative minima at: (Separate multiple answers by commas.) (Separate multiple answers by commas.) d) Find the x-value(s) where f'(x) has a relative maximum or minimum. f' has relative maxima at: f' has relative minima at: (Separate multiple answers by commas.) (Separate multiple answers by commas.) Instruction

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter4: Polynomial And Rational Functions
Section4.5: Rational Functions
Problem 7E
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**Calculus Problem Analysis** --- **Function:** \[ f(x) = x^3 + 4.5x^2 - 12x - 2 \] --- ### Instructions: - Use 'INF' to represent ∞ and '-INF' to represent -∞. - Use 'U' for the union symbol. - If an answer does not exist, enter DNE. ### Questions: #### a) Determine the intervals on which \( f \) is concave up and concave down. - \( f \) is concave up on: [Text box] - \( f \) is concave down on: [Text box] #### b) Based on your answer to part (a), determine the inflection points of \( f \). Each point should be entered as an ordered pair (that is, in the form \( (x, y) \)). [Text box] (Separate multiple answers by commas.) #### c) Find the critical numbers of \( f \) and use the Second Derivative Test, when possible, to determine the relative extrema. List only the \( x \)-coordinates. - Relative maxima at: [Text box] (Separate multiple answers by commas.) - Relative minima at: [Text box] (Separate multiple answers by commas.) #### d) Find the \( x \)-value(s) where \( f'(x) \) has a relative maximum or minimum. - \( f' \) has a relative maximum at: [Text box] (Separate multiple answers by commas.) - \( f' \) has a relative minimum at: [Text box] (Separate multiple answers by commas.) --- This analysis will guide you through finding concavity intervals, inflection points, critical numbers, and relative extrema of the given function \( f(x) \), enhancing your understanding of calculus concepts. **[Instructions]**
Transcribed Image Text:**Calculus Problem Analysis** --- **Function:** \[ f(x) = x^3 + 4.5x^2 - 12x - 2 \] --- ### Instructions: - Use 'INF' to represent ∞ and '-INF' to represent -∞. - Use 'U' for the union symbol. - If an answer does not exist, enter DNE. ### Questions: #### a) Determine the intervals on which \( f \) is concave up and concave down. - \( f \) is concave up on: [Text box] - \( f \) is concave down on: [Text box] #### b) Based on your answer to part (a), determine the inflection points of \( f \). Each point should be entered as an ordered pair (that is, in the form \( (x, y) \)). [Text box] (Separate multiple answers by commas.) #### c) Find the critical numbers of \( f \) and use the Second Derivative Test, when possible, to determine the relative extrema. List only the \( x \)-coordinates. - Relative maxima at: [Text box] (Separate multiple answers by commas.) - Relative minima at: [Text box] (Separate multiple answers by commas.) #### d) Find the \( x \)-value(s) where \( f'(x) \) has a relative maximum or minimum. - \( f' \) has a relative maximum at: [Text box] (Separate multiple answers by commas.) - \( f' \) has a relative minimum at: [Text box] (Separate multiple answers by commas.) --- This analysis will guide you through finding concavity intervals, inflection points, critical numbers, and relative extrema of the given function \( f(x) \), enhancing your understanding of calculus concepts. **[Instructions]**
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