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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Question
![### Function Analysis: \( f(x) = (x + 3)(x - 1)^2 \)
#### (A) Finding Critical Values
You are asked to find all critical values of the function \( f \). If there are no critical values, enter -1000. If there are more than one, enter them separated by commas.
\[ \text{Critical value(s)} = \_\_\_\_\_\_\_\_\_ \]
#### (B) Indicating Increasing Intervals
Use interval notation to indicate where the function \( f(x) \) is increasing.
**Note:** When using interval notation in WeBWorK, use `I` for \( \infty \), `-I` for \( -\infty \), and `U` for the union symbol. If there are no values that satisfy the required condition, enter "{}" without quotation marks.
\[ \text{Increasing:} = \_\_\_\_\_\_\_\_\_ \]
#### (C) Indicating Decreasing Intervals
Use interval notation to indicate where the function \( f(x) \) is decreasing.
\[ \text{Decreasing:} = \_\_\_\_\_\_\_\_\_ \]
#### (D) Finding Local Maxima
Find the \( x \)-coordinates of all local maxima of the function \( f \). If there are no local maxima, enter -1000. If there are more than one, enter them separated by commas.
\[ \text{Local maxima at } x = \_\_\_\_\_\_\_\_\_ \]
#### (E) Finding Local Minima
Find the \( x \)-coordinates of all local minima of the function \( f \). If there are no local minima, enter -1000. If there are more than one, enter them separated by commas.
\[ \text{Local minima at } x = \_\_\_\_\_\_\_\_\_ \]
#### (F) Indicating Concave Up Intervals
Use interval notation to indicate where the function \( f(x) \) is concave up.
\[ \text{Concave up:} = \_\_\_\_\_\_\_\_\_ \]
#### (G) Indicating Concave Down Intervals
Use interval notation to indicate where the function \( f(x) \) is concave down.
\[ \text{Concave down:} = \_\_\_\_\_\_\](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F98a85d3f-1221-4cd9-b5c2-c225eed9a46f%2F260db02c-e093-4846-8a2e-3839612c55d0%2Fmec8q2.png&w=3840&q=75)
Transcribed Image Text:### Function Analysis: \( f(x) = (x + 3)(x - 1)^2 \)
#### (A) Finding Critical Values
You are asked to find all critical values of the function \( f \). If there are no critical values, enter -1000. If there are more than one, enter them separated by commas.
\[ \text{Critical value(s)} = \_\_\_\_\_\_\_\_\_ \]
#### (B) Indicating Increasing Intervals
Use interval notation to indicate where the function \( f(x) \) is increasing.
**Note:** When using interval notation in WeBWorK, use `I` for \( \infty \), `-I` for \( -\infty \), and `U` for the union symbol. If there are no values that satisfy the required condition, enter "{}" without quotation marks.
\[ \text{Increasing:} = \_\_\_\_\_\_\_\_\_ \]
#### (C) Indicating Decreasing Intervals
Use interval notation to indicate where the function \( f(x) \) is decreasing.
\[ \text{Decreasing:} = \_\_\_\_\_\_\_\_\_ \]
#### (D) Finding Local Maxima
Find the \( x \)-coordinates of all local maxima of the function \( f \). If there are no local maxima, enter -1000. If there are more than one, enter them separated by commas.
\[ \text{Local maxima at } x = \_\_\_\_\_\_\_\_\_ \]
#### (E) Finding Local Minima
Find the \( x \)-coordinates of all local minima of the function \( f \). If there are no local minima, enter -1000. If there are more than one, enter them separated by commas.
\[ \text{Local minima at } x = \_\_\_\_\_\_\_\_\_ \]
#### (F) Indicating Concave Up Intervals
Use interval notation to indicate where the function \( f(x) \) is concave up.
\[ \text{Concave up:} = \_\_\_\_\_\_\_\_\_ \]
#### (G) Indicating Concave Down Intervals
Use interval notation to indicate where the function \( f(x) \) is concave down.
\[ \text{Concave down:} = \_\_\_\_\_\_\
Expert Solution
Step 1
Given function
Find the critical values for the given function. To find critical values we need to take derivative
Step 2
Apply product rule to find derivative
Step 3
Set the derivative =0 and solve for x
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