Get Instant Help From 5000+ Experts For
question

Writing Get your essay and assignment written from scratch by PhD expert

Rewriting: Paraphrase or rewrite your friend's essay with similar meaning at reduced cost

Editing:Proofread your work by experts and improve grade at Lowest cost

loader
Phone no. Missing!

Enter phone no. to receive critical updates and urgent messages !

Add File

Error goes here

Files Missing!

Please upload all relevant files for quick & complete assistance.

Guaranteed Higher Grade!

Calculation Of Local Maximum And Minimum Points With Characteristic Polynomial And Prime-Like Numbers

4 Pages / 861 Words Published On: 13-11-2020

Local Maximum and Minimum Points

where x ∈ [−2, 3]. (a) What is f 0 (x)? [1] (b) What is f 00(x)? [1] (c) Find all the stationary points of f. Find the value of f(x) at each stationary point. [2] (d) For each stationary point of f, find whether it is a local minimum, a local maximum or neither. [2] (e) Find all the global minima and maxima of f in the interval [−2, 3]. [2] 2. Let M = 1 6 1 0 (a) Find the eigenvalues of M. [3] (b) Find one eigenvector of M with respect to each eigenvalue. [3]

(c) Diagonalize M, i.e., write M in the form M = NDN −1 , where D is a diagonal matrix. [2] 3. X is a continuous random variable with density f where f(x) = x + x 2 + x 5 for x ∈ [0, 1] and f(x) = 0 elsewhere. What is the probability of the event {X > 1/2}? [6] 4. Suppose you want to launch your startup in some innovative area. Currently, there exist two enterprises A and B competing for this market. You want to find out their investment strategies (which are given by real numbers a, b) prior to commiting into the competition.

A friend who works in A told you that their profit is given by p(a, b) = ab2 − a 2 + b 2 + 6b − 9a + 10, but unfortunately he does not know the values of a, b. He also mentioned that both enterprises are apparently not very good in keeping secrets, so the function f(x) = p(x, b) achieves the maximum value at point x = a, while x = b minimises g(x) = p(a, x). Use this information to find a and b [8] 5. A positive integer is called prime-like if it is not divisible by 2 and not divisible by 5.

(a) How many prime-like numbers with 4 digits (from 1000 to 9999)? [2] (b) How many prime-like numbers with 4 digits have at least one even digit? [3]

(c) How many prime-like numbers with 4 digits are not divisible by 3? [4] 6. Let Y be a random variable uniformly distributed on the set {−1, 0, 1, 2}. Let U1, U2 be the random variables defined by U1 = Y 2 − Y and U2 = Y 2−1 Y 3−2 . (a) Find the expected values of U1 and U2. [2] (b) Find variances of U1 and U2. [2] (c) Is U1 independent of U2? Justify your answer. [2] 7. A fair 6-sided die is rolled three times. (a) Find the probability that the sum of all three outcomes equals 8.

[4] (b) Find the probability that the first roll was 1 given that the sum of outcomes equals 8. [3] 8. Eight students Alice, Bob, Casey, Drew, Eva, Francis, Glen, Hunter entered Monash University this year. Alice, Bob and Casey are from Canberra and Drew, Eva, Francis are from Newcastle.

Glen and Hunter are international students from different countries. Alice, Casey and Hunter practice tennis, while Drew, Francis, Glen and Hunter practice soccer. Any two students from the same city or practicing the same sport know each other. (a) Draw a graph corresponding to the student acquaintances. Find its number of edges.

[2] (b) Write down the adjacency matrix for this graph. Does it contain a spanning tree? [3] (c) Is it possible to seat all eight students at a round table in such a way that any of them knows both neighbours. Justify your answer. [3]

Cite This Work

To export a reference to this article please select a referencing stye below:

My Assignment Help. (2020). Calculation Of Local Maximum And Minimum Points With Characteristic Polynomial And Prime-Like Numbers. Retrieved from https://myassignmenthelp.com/free-samples/mat9004-practice-exam/quadratic-equation.html.

"Calculation Of Local Maximum And Minimum Points With Characteristic Polynomial And Prime-Like Numbers." My Assignment Help, 2020, https://myassignmenthelp.com/free-samples/mat9004-practice-exam/quadratic-equation.html.

My Assignment Help (2020) Calculation Of Local Maximum And Minimum Points With Characteristic Polynomial And Prime-Like Numbers [Online]. Available from: https://myassignmenthelp.com/free-samples/mat9004-practice-exam/quadratic-equation.html
[Accessed 02 October 2023].

My Assignment Help. 'Calculation Of Local Maximum And Minimum Points With Characteristic Polynomial And Prime-Like Numbers' (My Assignment Help, 2020) <https://myassignmenthelp.com/free-samples/mat9004-practice-exam/quadratic-equation.html> accessed 02 October 2023.

My Assignment Help. Calculation Of Local Maximum And Minimum Points With Characteristic Polynomial And Prime-Like Numbers [Internet]. My Assignment Help. 2020 [cited 02 October 2023]. Available from: https://myassignmenthelp.com/free-samples/mat9004-practice-exam/quadratic-equation.html.


Stuck on Any Question

Our best expert will help you with the answer of your question with best explanation.

question

Writing: Get your essay and assignment written from scratch by PhD expert

Rewriting: Paraphrase or rewrite your friend's essay with similar meaning at reduced cost

Editing: Proofread your work by experts and improve grade at Lowest cost

question
We will use e-mail only for:

arrow Communication regarding your orders

arrow To send you invoices, and other billing info

arrow To provide you with information of offers and other benefits

Phone no. Missing!

Enter phone no. to receive critical updates and urgent messages !

loader
250 words
Error goes here

Error goes here

Files Missing!

Please upload all relevant files for quick & complete assistance.

icon
5% Cashback

On APP - grab it while it lasts!

Download app now (or) Scan the QR code

*Offer eligible for first 3 orders ordered through app!

screener
ribbon
callback request mobile
Have any Query?
close
Subtraction Payment required!

Only one step away from your solution of order no.