Consider the function f(x)= - 2x³ +36x²162x + 3. For this function there are three important open intervals: (-∞, A), (A, B), and (B, ∞o) where A and B are the critical numbers. Find A and B = For each of the following open intervals, determine whether f(x) is increasing or decreasing. (-∞, A): [Select an answer (A, B): [Select an answer (B, ∞): [Select an answer Using the First Derivative Test, we can conclude: at x = A, f(x) has a [Select an answer at x = B, f(x) has a Question Help: Submit Question Select an answer Select an answer Vid local maximum local minimum neither a max nor a min
Consider the function f(x)= - 2x³ +36x²162x + 3. For this function there are three important open intervals: (-∞, A), (A, B), and (B, ∞o) where A and B are the critical numbers. Find A and B = For each of the following open intervals, determine whether f(x) is increasing or decreasing. (-∞, A): [Select an answer (A, B): [Select an answer (B, ∞): [Select an answer Using the First Derivative Test, we can conclude: at x = A, f(x) has a [Select an answer at x = B, f(x) has a Question Help: Submit Question Select an answer Select an answer Vid local maximum local minimum neither a max nor a min
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![Consider the function \( f(x) = -2x^3 + 36x^2 - 162x + 3 \). For this function there are three important open intervals: \(( -\infty, A )\), \(( A, B )\), and \(( B, \infty )\) where \( A \) and \( B \) are the critical numbers.
Find \( A \)
and \( B \)
For each of the following open intervals, determine whether \( f(x) \) is increasing or decreasing.
\(( -\infty, A )\): [Select an answer]
\(( A, B )\): [Select an answer]
\(( B, \infty )\): [Select an answer]
Using the First Derivative Test, we can conclude:
At \( x = A \), \( f(x) \) has a [Select an answer]
At \( x = B \), \( f(x) \) has a [Select an answer]
Options for selection:
- local maximum
- local minimum
- neither a max nor a min
Question Help: [Video]
[Submit Question]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4df0d9d6-a5af-48e8-af07-cbf992b42454%2F1fa0b930-afeb-46e7-b51b-df1e60a70af3%2Fo6tnqkn_processed.png&w=3840&q=75)
Transcribed Image Text:Consider the function \( f(x) = -2x^3 + 36x^2 - 162x + 3 \). For this function there are three important open intervals: \(( -\infty, A )\), \(( A, B )\), and \(( B, \infty )\) where \( A \) and \( B \) are the critical numbers.
Find \( A \)
and \( B \)
For each of the following open intervals, determine whether \( f(x) \) is increasing or decreasing.
\(( -\infty, A )\): [Select an answer]
\(( A, B )\): [Select an answer]
\(( B, \infty )\): [Select an answer]
Using the First Derivative Test, we can conclude:
At \( x = A \), \( f(x) \) has a [Select an answer]
At \( x = B \), \( f(x) \) has a [Select an answer]
Options for selection:
- local maximum
- local minimum
- neither a max nor a min
Question Help: [Video]
[Submit Question]
Expert Solution
Step 1
The critical numbers of the function: is calculated by solving the equation: for x.
For any function: , the sign of its first derivative: changes from negative to positive at the local minimum. For any function: , the sign of its first derivative: changes from positive to negative at the local maximum.
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