Concept explainers
a
To determine the interval in which the polynomial function will definitely have real root with the help of graph and intermediate value theorem.
a
Answer to Problem 42RE
The required intervals are:
Explanation of Solution
Given:
Graph:
Using graphing utility, the graph of above function is,
Interpretation:
Using the graph, consider interval of length 1, then
f (-2) = 2 and f (-1) = -3.5
Since,
According to Intermediate value theorem, there will be a real root present in the interval
Again,
f (0) = -2 and f (1) = 3.5
Since,
According to Intermediate value theorem there will be a real root present in the interval
Conclusion:
Hence, in the intervals,
b
To estimate the real roots of the given function using the graph and verify it using the table properties of the graphing tool.
b
Answer to Problem 42RE
The real zeroes are: -1.9 and 0.74
Explanation of Solution
Given:
Graph:
Using graphing utility, the graph of above function is,
Interpretation:
From the graph, it clear that the curve intersects the x -axis at (-1.9, 0) and (0.74, 0), which means
that, -1.9 and 0.74 are the two real zeroes of the given polynomial function.
Verification of sub-part (a):
Table feature:
Graph:
When the above table and graph are compared, it is clear that, the zeros of the function are found in the interval which was considered in sub-part (a).
Conclusion:
Hence, the real zeroes of the function are -1.9 and 0.74.
Chapter 2 Solutions
Precalculus with Limits: A Graphing Approach
- Calculus: Early TranscendentalsCalculusISBN:9781285741550Author:James StewartPublisher:Cengage LearningThomas' Calculus (14th Edition)CalculusISBN:9780134438986Author:Joel R. Hass, Christopher E. Heil, Maurice D. WeirPublisher:PEARSONCalculus: Early Transcendentals (3rd Edition)CalculusISBN:9780134763644Author:William L. Briggs, Lyle Cochran, Bernard Gillett, Eric SchulzPublisher:PEARSON
- Calculus: Early TranscendentalsCalculusISBN:9781319050740Author:Jon Rogawski, Colin Adams, Robert FranzosaPublisher:W. H. FreemanCalculus: Early Transcendental FunctionsCalculusISBN:9781337552516Author:Ron Larson, Bruce H. EdwardsPublisher:Cengage Learning