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Extreme ValuesA graph that is large enough to show a
Chapter 4, Problem 13PE(choose chapter or problem)
Problem 13PE
Extreme Values
A graph that is large enough to show a function’s global behavior may fail to reveal important local features. The graph of is a case in point.
a. Graph ƒ over the interval .Where does the graph appear to have local extreme values or points of inflection?
b. Now factor and show that ƒ has a local maximum at and local minima at
c. Zoom in on the graph to find a viewing window that shows the presence of the extreme values at
The moral here is that without calculus the existence of two of the three extreme values would probably have gone unnoticed. On any normal graph of the function, the values would lie close enough together to fall within the dimensions of a single pixel on the screen.
Questions & Answers
QUESTION:
Problem 13PE
Extreme Values
A graph that is large enough to show a function’s global behavior may fail to reveal important local features. The graph of is a case in point.
a. Graph ƒ over the interval .Where does the graph appear to have local extreme values or points of inflection?
b. Now factor and show that ƒ has a local maximum at and local minima at
c. Zoom in on the graph to find a viewing window that shows the presence of the extreme values at
The moral here is that without calculus the existence of two of the three extreme values would probably have gone unnoticed. On any normal graph of the function, the values would lie close enough together to fall within the dimensions of a single pixel on the screen.
ANSWER:
Solution:
Step 1 of 4
In this problem, we have given that the function is
.