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Chapter 4.6, Problem 6E
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Single Variable Calculus: Early Tr...
8th Edition
James Stewart
ISBN: 9781305270343
BuyFindarrow_forward
Single Variable Calculus: Early Tr...
8th Edition
James Stewart
ISBN: 9781305270343
Textbook Problem
Produce graphs of f that reveal all the important aspects of the curve. In particular, you should use graphs of f′ and f″ to estimate the intervals of increase and decrease, extreme values, intervals of concavity, and inflection points.
f(x) = 6 sin x − x2, −5 ≤ x ≤ 3
To determine
To sketch: The graph of f that reveals all important aspects of the curve and the graph of
Explanation
Given information:
The curve function is
The interval lies in
Calculation:
Draw the graph of the function f by substituting different values for x.
The sketch of the function f is shown in Figure 1.
Differentiate Equation (1) with respect to x.
The sketch of the function
Differentiate Equation (2) with respect to x.
The sketch of the function
Refer Figure 2.
The curve f is decreasing on
The curve f is increasing on
The local maximum value occurs at
The local minimum value occurs at
Therefore, the intervals of increase is on
Therefore, the interval of decrease is on
Find the extreme values as shown below:
Substitute
Therefore, the maximum value is
Chapter 4 Solutions
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Suppose that 30% of all automobiles undergoing an emissions inspection at an inspection station fail the inspec...
Introduction To Statistics And Data Analysis
Describe the process of conducting a literature search, including using an online database such as PsycINFO, an...
Research Methods for the Behavioral Sciences (MindTap Course List)
