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Determine the intervals on which the function is concave up or down and find the points of inflection. y = 5x? + In(x) (x > 0)

Determine the intervals on which the function is concave up or down and find the points of inflection. y = 5x? + In(x) (x > 0)

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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**Determine the intervals on which the function is concave up or down and find the points of inflection.** \( y = 5x^2 + \ln(x) \quad (x > 0) \) Provide intervals in the form \((\ast , \ast )\). Use the symbol \(\infty\) for infinity, \(\cup\) for combining intervals, and an appropriate type of parenthesis "(", ")", "[", or "]", depending on whether the interval is open or closed. Enter \(\varnothing\) if the interval is empty. Provide points of inflection as a comma-separated list of \((x, y)\) ordered pairs. If the function does not have any inflection points, enter DNE. Use exact values for all responses. - **Concave up:** [Textbox] - **Concave down:** [Textbox] - \((x, y) =\) [Textbox]
Transcribed Image Text:**Determine the intervals on which the function is concave up or down and find the points of inflection.** \( y = 5x^2 + \ln(x) \quad (x > 0) \) Provide intervals in the form \((\ast , \ast )\). Use the symbol \(\infty\) for infinity, \(\cup\) for combining intervals, and an appropriate type of parenthesis "(", ")", "[", or "]", depending on whether the interval is open or closed. Enter \(\varnothing\) if the interval is empty. Provide points of inflection as a comma-separated list of \((x, y)\) ordered pairs. If the function does not have any inflection points, enter DNE. Use exact values for all responses. - **Concave up:** [Textbox] - **Concave down:** [Textbox] - \((x, y) =\) [Textbox]
Expert Solution
Step 1

Given
y = 5x2 + ln x
where x > 0

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