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Perform a first derivative test on the function f(x) = 2x³ + 3x² - 36x +4; [-3,5]. a. Locate the critical points of the given function. b. Use the first derivative test to locate the local maximum and minimum values. c. Identify the absolute minimum and maximum values of the function on the given interval (when they exist). The Chical points are locale a (Use a comma to separate answers as needed.) OB. There are no critical points. b. Locate the local maximum and minimum values. Select the correct choice below and, if necessary, fill in the answer box(es) within your choice. OA. There are local maximum(s) at x = -3 and local minimum(s) at x = -2. (Use a comma to separate answers as needed.) OB. There are local minimum(s) at x = (Use a comma to separate answers as needed.) OC. There are local maximum(s) at x = There are no local maximums. I There are no local minimums. (Use a comma to separate answers as needed.) O D. There are no local maximums nor local minimums. Help me solve this View an example O Tyne here to search Get more help . Part 2 of 3 HI Media O 000

Perform a first derivative test on the function f(x) = 2x³ + 3x² - 36x +4; [-3,5]. a. Locate the critical points of the given function. b. Use the first derivative test to locate the local maximum and minimum values. c. Identify the absolute minimum and maximum values of the function on the given interval (when they exist). The Chical points are locale a (Use a comma to separate answers as needed.) OB. There are no critical points. b. Locate the local maximum and minimum values. Select the correct choice below and, if necessary, fill in the answer box(es) within your choice. OA. There are local maximum(s) at x = -3 and local minimum(s) at x = -2. (Use a comma to separate answers as needed.) OB. There are local minimum(s) at x = (Use a comma to separate answers as needed.) OC. There are local maximum(s) at x = There are no local maximums. I There are no local minimums. (Use a comma to separate answers as needed.) O D. There are no local maximums nor local minimums. Help me solve this View an example O Tyne here to search Get more help . Part 2 of 3 HI Media O 000

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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**Perform a First Derivative Test on the Function f(x) = 2x³ + 3x² - 36x + 4 Over the Interval [-3, 5]** ### a. Locate the Critical Points of the Given Function - - - - - - - - - - - - - - - - (The solution and steps to solving this would appear here.) *Multiple-choice options:* 1. ( ) The critical point(s) is/are located at x = 2. - (Use a comma to separate answers as needed.) 2. ( ) There are no critical points. ### b. Use the First Derivative Test to Locate the Local Maximum and Minimum Values - - - - - - - - - - - - - - - - - - - - - - - - - - *Multiple-choice options:* 1. (●) A. There are local maximum(s) at x = -3 and local minimum(s) at x = 2. - (Use a comma to separate answers as needed.) 2. ( ) B. There are local minimum(s) at x = ______. There are no local maximums. - (Use a comma to separate answers as needed.) 3. ( ) C. There are local maximum(s) at x = ______. There are no local minimums. - (Use a comma to separate answers as needed.) 4. ( ) D. There are no local maximums nor local minimums. ### c. Identify the Absolute Minimum and Maximum Values of the Function on the Given Interval (When They Exist) - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - (The solution and steps to solving this would appear here.) ### Explanation of Diagrams or Graphs There are no diagrams or graphs present in the image. *Additional Options for Assistance:* 1. **Help me solve this** 2. **View an example** 3. **Get more help** 4. **Media** (Dropdown menu) *(The image is an interface most likely from an online educational platform where students can attempt solving calculus problems related to the first derivative test and receive immediate feedback or additional help as needed.)* For more details, visit our educational resources or contact our support for personalized assistance.
Transcribed Image Text:**Perform a First Derivative Test on the Function f(x) = 2x³ + 3x² - 36x + 4 Over the Interval [-3, 5]** ### a. Locate the Critical Points of the Given Function - - - - - - - - - - - - - - - - (The solution and steps to solving this would appear here.) *Multiple-choice options:* 1. ( ) The critical point(s) is/are located at x = 2. - (Use a comma to separate answers as needed.) 2. ( ) There are no critical points. ### b. Use the First Derivative Test to Locate the Local Maximum and Minimum Values - - - - - - - - - - - - - - - - - - - - - - - - - - *Multiple-choice options:* 1. (●) A. There are local maximum(s) at x = -3 and local minimum(s) at x = 2. - (Use a comma to separate answers as needed.) 2. ( ) B. There are local minimum(s) at x = ______. There are no local maximums. - (Use a comma to separate answers as needed.) 3. ( ) C. There are local maximum(s) at x = ______. There are no local minimums. - (Use a comma to separate answers as needed.) 4. ( ) D. There are no local maximums nor local minimums. ### c. Identify the Absolute Minimum and Maximum Values of the Function on the Given Interval (When They Exist) - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - (The solution and steps to solving this would appear here.) ### Explanation of Diagrams or Graphs There are no diagrams or graphs present in the image. *Additional Options for Assistance:* 1. **Help me solve this** 2. **View an example** 3. **Get more help** 4. **Media** (Dropdown menu) *(The image is an interface most likely from an online educational platform where students can attempt solving calculus problems related to the first derivative test and receive immediate feedback or additional help as needed.)* For more details, visit our educational resources or contact our support for personalized assistance.
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