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=f"(x) = 2x−3+ 36x-4 + 12x-5

=f"(x) = 2x−3+ 36x-4 + 12x-5

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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Consider the function below.
f(x) = 1 + 
1
x
 + 
6
x2
 + 
1
x3
Produce a graph of f that reveal all the important aspects of the curve. Estimate the intervals of increase and decrease and intervals of concavity, and use calculus to find these intervals.
Step 6 larger x-value X = −9+5√3 Step 7 Factoring this, we get f"(x): when x² + 18x + 6 = 0, or when we have the following. smaller x-value X = -9-5√3 -9-5√3 When x E -80, so f(x) is concave down +36x-4 + 12x = 2x When x E (-⁹ -9 f(x) is concave up -9 √75 and when x E -9 + 75, -9 + up -5 down 2 +5(+2 = 5√3-9 Submit Skip (you cannot come back) + + 18x + 6). Since 2 75 and when x € (0, ∞), we have f"(x) is positive is never 0, then f"(x) = 0 √75,0), we have f"(x) is negative Step 8 Find the interval where the function is concave up. (Enter your answer using interval notation.) negative and positive Find the interval where the function is concave down. (Enter your answer using interval notation.) I and so
Transcribed Image Text:Step 6 larger x-value X = −9+5√3 Step 7 Factoring this, we get f"(x): when x² + 18x + 6 = 0, or when we have the following. smaller x-value X = -9-5√3 -9-5√3 When x E -80, so f(x) is concave down +36x-4 + 12x = 2x When x E (-⁹ -9 f(x) is concave up -9 √75 and when x E -9 + 75, -9 + up -5 down 2 +5(+2 = 5√3-9 Submit Skip (you cannot come back) + + 18x + 6). Since 2 75 and when x € (0, ∞), we have f"(x) is positive is never 0, then f"(x) = 0 √75,0), we have f"(x) is negative Step 8 Find the interval where the function is concave up. (Enter your answer using interval notation.) negative and positive Find the interval where the function is concave down. (Enter your answer using interval notation.) I and so
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