2. Let f(x)=x-3x² a. Determine all x-values where f(x)=0 b. Fill in the table below with the intervals of concavity. Select a test value for each interval and evaluate f"(x) for each test value. Finally, decide whether the function is concave up or concave down on each interval. Intervals Test value Conclusion c. Find the points of inflection of the graph of f(x).

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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2. Let f(x)=x-3x²
a. Determine all x-values where f"(x) = 0
b. Fill in the table below with the intervals of concavity. Select a test value for each interval and evaluate
f"(x) for each test value. Finally, decide whether the function is concave up or concave down on each
interval.
Intervals
Test value
f" (x)
Conclusion
c. Find the points of inflection of the graph of f(x).
Transcribed Image Text:2. Let f(x)=x-3x² a. Determine all x-values where f"(x) = 0 b. Fill in the table below with the intervals of concavity. Select a test value for each interval and evaluate f"(x) for each test value. Finally, decide whether the function is concave up or concave down on each interval. Intervals Test value f" (x) Conclusion c. Find the points of inflection of the graph of f(x).
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