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Finding Relative Extrema

Finding Relative Extrema

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter6: Applications Of The Derivative
Section6.CR: Chapter 6 Review
Problem 1CR
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Finding Relative Extrema
4 1. For the function f(x)=x+-, perform each of the following steps: i. State the domain of the function. ii. Find any critical numbers. (Note: x = 0 is not a critical point of this function, since it is not in the domain, so you do not need to try to classify it as a relative minimum / maximum.) iii. Use the First Derivative Test (create a sign chart) to classify each critical number as a relative minimum, relative maximum, or neither (show work). iv. Find the points on the graph corresponding to the relative minimum / maximum. v. Use the Second Derivative Test to confirm the results from part (iii). vi. Use the second derivative to find the intervals where the graph is concave up / concave down. vii. Does the graph of f(x) contain any inflection points? Explain why or why not. viii. Use the information found in parts (i – vii) to sketch a graph of the function.
Transcribed Image Text:4 1. For the function f(x)=x+-, perform each of the following steps: i. State the domain of the function. ii. Find any critical numbers. (Note: x = 0 is not a critical point of this function, since it is not in the domain, so you do not need to try to classify it as a relative minimum / maximum.) iii. Use the First Derivative Test (create a sign chart) to classify each critical number as a relative minimum, relative maximum, or neither (show work). iv. Find the points on the graph corresponding to the relative minimum / maximum. v. Use the Second Derivative Test to confirm the results from part (iii). vi. Use the second derivative to find the intervals where the graph is concave up / concave down. vii. Does the graph of f(x) contain any inflection points? Explain why or why not. viii. Use the information found in parts (i – vii) to sketch a graph of the function.
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