Reference no: EM131119414
1. Use the Intermediate Value Theorem and Rolle's Theorem to prove that the equation x4 + 2x2 - 2 = 0 has exactly one real solution on the interval 0 < x < 1.
2. Consider the cubic function f (x) = ax3 + bx2 + cx + d, where a ≠ 0.
Prove that f can have zero, one, or two critical numbers, and give an example for each.
3. Assume that f is continuous on [-1,3] and differentiable on (-1,3). Assume also that f (-1) = 5 and f(3) = -1. Examine each of the following statements. If always true, say so, and cite a relevant theorem or fact to support your answer. If false (false means "not always true") then say so, and either explain your answer or give a counter example.
(a) There exists a number c ∈ (-1, 3) such that f'(c) = 3/2.
(b) If k ∈ (-1, 5), then there exists a number c ∈ (-1,3) such that f(c) = k.
(c) If c ∈ (-1,3), f'(c) = 0 & f"(c) = 0, then f(c) is a maximum or minimum on [-1,3].
|
Define determinism - fatalism and free will
: Distinguish between natural (scientific) determinism and theological (religious) determinism. Discuss whether or not you believe free will and determinism can be compatible.
|
|
Discuss the program and what led to its implementation
: Briefly discuss the program and what led to its implementation. In general, what are the different types of program evaluation available to a manager
|
|
The most influential quality of highly effective educators
: The disposition to teach has been identified as the most influential quality of highly effective educators. Dispositions are the values, commitments, and professional ethics that influence behaviors toward students, families, colleagues, and commu..
|
|
Example of healthcare partnership in your community
: Discuss an example of a healthcare partnership in your community and specifically cite examples that show how nurses, both individually and collectively, influenced the care provided. What obstacles were/are confronted, and what strategies were/are e..
|
|
Intermediate value theorem and rolles theorem
: Examine each of the statements - Intermediate Value Theorem and Rolles Theorem
|
|
Question regarding the containing contraband
: Using the CSU Library, choose the Criminal Justice link. In the search box, input Containing Contraband, then select the option in the list that comes up, by author Michael Grohs, entitled "Containing Contraband."
|
|
Sequential operations-what is unit cost for acceptable part
: In the production of a part for a printer, four sequential operations are involved. Unit processing costs for the operations are $10, $6, $15, and $20, respectively. If no inspection is performed, what is the unit cost for an acceptable part? Assume ..
|
|
Describe the structure of dna
: The structure to describe the structure of DNA and how it carries genetic information. Their studies showed that gene therapy can cure inherited disease
|
|
What is the role of effective communication in leadership
: Interview a leader of choice. Examples of leaders can include, but are not limited to, former or current managers or supervisors, educational leaders, civic/business leaders, and religious leaders. This interview can take place via phone, via e-m..
|