Posted Mar 24, 2020 11:13 AM 1. P(x) = -x^3 + 3x^2 + 24x -3 decreases on (-infinity,-2). What does it do after that (to the right of -2 on the x-axis)? 2. What is the max of P(x) (y-value of its relative maximum point), and where is its min (x-value of its relative minimum point)? 3. Warning! At least one problem on the final exam will ask where the graph is smiling (concave up) or where the graph is frowning (concave down) or where the smile and the frown meet (inflection point). When this happens (and it will!) the plus signs and the minus signs on the number linç MUST BE DETERMINED BY THE SECOND DERIVATIVE (instead of the 1st). The 1st derivative of P(x) is -3x^2 + 6x +24. The 2nd is -6x + 6. So, based on the SECOND DERIVATIVE, my plus signs tell me that the graph is smiling (concave up) on (-infinity, ?). 4. Again, based on the SECOND DERIVATIVE, my minus signs tell me that the graph is frowning (concave down) on (?, infinity). 5. Where is the meeting place (inflection point) of the smile and the frown? REMINDER! Please answer all 5 questions in one very important email =) DE

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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Posted Mar 24, 2020 11:13 AM
1. P(x) = -x^3 + 3x^2 + 24x -3 decreases on (-infinity,-2). What does it do after that
(to the right of -2 on the x-axis)?
2. What is the max of P(x) (y-value of its relative maximum point), and where is its
min (x-value of its relative minimum point)?
3. Warning! At least one problem on the final exam will ask where the graph is
smiling (concave up) or where the graph is frowning (concave down) or where the
smile and the frown meet (inflection point). When this happens (and it will!) the plus
signs and the minus signs on the number linç MUST BE DETERMINED BY THE
SECOND DERIVATIVE (instead of the 1st). The 1st derivative of P(x) is -3x^2 + 6x
+24. The 2nd is -6x + 6. So, based on the SECOND DERIVATIVE, my plus signs tell
me that the graph is smiling (concave up) on (-infinity, ?).
4. Again, based on the SECOND DERIVATIVE, my minus signs tell me that the graph
is frowning (concave down) on (?, infinity).
5. Where is the meeting place (inflection point) of the smile and the frown?
REMINDER! Please answer all 5 questions in one very important email =) DE
Transcribed Image Text:Posted Mar 24, 2020 11:13 AM 1. P(x) = -x^3 + 3x^2 + 24x -3 decreases on (-infinity,-2). What does it do after that (to the right of -2 on the x-axis)? 2. What is the max of P(x) (y-value of its relative maximum point), and where is its min (x-value of its relative minimum point)? 3. Warning! At least one problem on the final exam will ask where the graph is smiling (concave up) or where the graph is frowning (concave down) or where the smile and the frown meet (inflection point). When this happens (and it will!) the plus signs and the minus signs on the number linç MUST BE DETERMINED BY THE SECOND DERIVATIVE (instead of the 1st). The 1st derivative of P(x) is -3x^2 + 6x +24. The 2nd is -6x + 6. So, based on the SECOND DERIVATIVE, my plus signs tell me that the graph is smiling (concave up) on (-infinity, ?). 4. Again, based on the SECOND DERIVATIVE, my minus signs tell me that the graph is frowning (concave down) on (?, infinity). 5. Where is the meeting place (inflection point) of the smile and the frown? REMINDER! Please answer all 5 questions in one very important email =) DE
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