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 41RE
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 (-3) = -0.08 and f (-2) = 1.88
Since,
According to Intermediate value theorem there will be a real root present in the interval
Again,
f (-1) = 0.96 and f (0) = -1.4
Since,
According to Intermediate value theorem there will be a real root present in the interval
And,
f (3) = -2.72 and f (4) = 3.56
Since,
According to Intermediate value theorem there will be definitely 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 41RE
The real zeroes are: -2.98, -0.55 and 3.53
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 (-2.98, 0), (-0.55, 0) and (3.53, 0), which means that, -2.98, -0.55 and 3.53 are the three 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 -2.98, -0.55 and 3.53.
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