Chapter 4.6, Problem 2E
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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) = −2x6 + 5x5 + 140x3 − 110x2
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
Calculation:
Equate Equation (1) equal to 0.
Solve Equation (2).
Draw the graph of the function f by substituting different values for x.
The sketches of the function f with the important aspects are shown in Figure 1 and Figure 2.
Differentiate Equation (1) with respect to x.
Equate Equation (3) equal to 0.
Solve Equation (4).
The sketches of the function
Differentiate Equation (3) with respect to x.
Equate Equation (5) equal to 0.
Solve Equation (6).
The sketch of the function
Refer Figure 3 and Figure 4.
The curve f is decreasing on
The curve f is increasing on
The local minimum value occurs at
The local maximum value occurs at
Therefore, the intervals of increase is on
Therefore, the intervals of decrease is on
Chapter 4 Solutions
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Two shipping services offer overnight delivery of parcels, and both promise delivery before 10 A.M. A mail-orde...
Introduction To Statistics And Data Analysis
Analyzing a Critical Number A differentiable function f has one critical number at x=5. Identify the relative e...
Calculus (MindTap Course List)
