Concept explainers
a.
To find: the absolute extrema of f and where they occur.
a.
Answer to Problem 51E
The absolute maximum is
Explanation of Solution
Given information: f is continuous on
x | 0 | 1 | 2 | 3 |
f | 1 | 2 | 0 | −2 |
f’ | 3 | 0 | Does not exist | −3 |
f’’ | 0 | −1 | Does not exist | 0 |
x | 0 < x < 1 | 1 < x < 2 | 2 < x < 3 |
f | + | + | − |
f’ | + | − | − |
f’’ | − | − | − |
The tables shows that,
The derivative of 1 is 0,
Hence, the absolute maximum is
b.
To find: the points of inflection.
b.
Answer to Problem 51E
There are no points of inflection.
Explanation of Solution
Given information: f is continuous on
x | 0 | 1 | 2 | 3 |
f | 1 | 2 | 0 | −2 |
f’ | 3 | 0 | Does not exist | −3 |
f’’ | 0 | −1 | Does not exist | 0 |
x | 0 < x < 1 | 1 < x < 2 | 2 < x < 3 |
f | + | + | − |
f’ | + | − | − |
f’’ | − | − | − |
The provided information shows that the function is always concave down, that is
Hence, there are no points of inflection.
c.
To graph: the function f with the provided information.
c.
Explanation of Solution
Given information: f is continuous on
x | 0 | 1 | 2 | 3 |
f | 1 | 2 | 0 | −2 |
f’ | 3 | 0 | Does not exist | −3 |
f’’ | 0 | −1 | Does not exist | 0 |
X | 0 < x < 1 | 1 < x < 2 | 2 < x < 3 |
F | + | + | − |
f’ | + | − | − |
f’’ | − | − | − |
Graph:
Interpretation:
Hence, this is the probable graph for function f with the provided information.
Chapter 5 Solutions
Calculus 2012 Student Edition (by Finney/Demana/Waits/Kennedy)
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