Math paper on either application of differentiation or the application of integration with two worked out examples. 500 words needed. Paper on application of differentiation or the application of integration. You should have two worked-out examples. For example, Maximize a profit function or Minimize a cost function or maximize a revenue function. These are applications of the derivative. Application of integration: find the average value of a function, find the volume of a solid of revolution, etc. You may choose other applications; it is up to you. I just stated some examples. In your project, first, you introduce the concept and describe it, then you will do the examples, that is, the application of the concept. Your paper should also have references. Your project should be typed.

Write a 3- to 5-paragraphs critique of the article (2 to 3 pages). In your critique, include responses to the following:Why did the authors use multiple regression?Do you think it’s the most appropriate choice? Why or why not?Did the authors display the data?Do the results stand alone? Why or why not?Did the authors report effect size? If yes, is this meaningful?Use proper APA format, citations, and referencing.

Module 4 AssignmentIn this assignment, you will apply what you've learned in this module about the designs of experiments to a sample data set and scenario.Assignment InstructionsConsider the following: The ABC Company wants to optimize the response (click rate) to their online ads. After a brainstorming session, thirteen factors were identified as potentially having an effect on the response (click) rate. The table below lists the 13 factors and the two levels that should be considered. This data is available in the DOE Assignment JMP file attached below. Identified Response FactorsTeaser OfferTelephoneNumberGraphicFont SizeAdvertisingChanelMessageTypeHeadlineLayoutProductselectionGift OfferProduc InfoColorSchemaDiscountNumber ofClicksLevel 1YesYesYesLargeYesAHeadline 1StandardFeature AYesVersion AAYesLevel 2NoNoNoSmallNoBHeadline 2CreativeFeature BNoVersion BBNo1YesYesYesLargeYesAHeadline 1StandardFeature AYesVersion AAYes522NoYesNoLargeYesBHeadline2CreativeFeature AYesVersion BANo383YesNoNoSmallYesBHeadline 1StandardFeature BYesVersion BBNo424YesYesYesSmallNoBHeadline 1CreativeFeature ANoVersion BBYes1345NoYesYesLargeNoBHeadline 1CreativeFeature BYesVersion BBYes1046NoNoNoLargeYesAHeadline 1CreativeFeature ANoVersion ABYes607NoNoYesSmallYesAHeadline 2CreativeFeature BYesVersion BAYes618NoNoYesLargeNoBHeadline 2StandardFeature BNoVersion ABNo689YesNoNoLargeYesBHeadline 1StandardFeature BNoVersion BAYes5710NoYesNoSmallYesAHeadline 1CreativeFeature BNoVersion ABNo3011YesNoNoSmallNoBHeadline 2CreativeFeature ANoVersion AAYes10812NoYesNoSmallNoBHeadline 1StandardFeature AYesVersion AANo3913YesNoYesSmallNoAHeadline 1CreativeFeature BYesVersion AANo4014YesYesNoLargeNoAHeadline 2CreativeFeature BNoVersion BANo4915YesYesYesSmallYesAHeadline 2StandardFeature ANoVersion BBNo3716YesYesNoLargeNoAHeadline 2StandardFeature BYesVersion ABYes9917NoYesYesSmallYesBHeadline 2StandardFeature BNoVersion AAYes8618NoNoYesLargeNoAHeadline 1StandardFeature ANoVersion BANo4319YesNoYesLargeYesBHeadline 2CreativeFeature AYesVersion ABNo4720NoNoNoSmallNoAHeadline 2StandardFeature AYesVersion BBYes104Discuss how you approach the problems and answer the questions along the way.1. How many treatments do you need at a minimum to estimate 13 main effects and the overall mean? Find a design using JMP DOE>Classical Designs>Screening Designs add 13 factors and find a design.What is the minimum number of treatments (runs)?What is the fractional factorial design with the smallest number of runs you can use for our problem?Which other design could you choose?2. Once you have a design matrix you would carry out the treatments and collect the response for each treatment (run). To exercise the analysis of a design I provided you with a 20 run design (which is the Packett-Burman design shown ion your list) which has responses provided in the JMP file. Use the design matrix provided in the DOE_Assignment_5_Click(2).jmp file with the number of clicks as the response variable. Use DOE>Classical>Two Level Screening> Fit Two Level Screening . Which factors are statistically significant at p<=0.05? Highlight the statistically significant factor rows (use individual p) and click run model. Interpret the output. 3. To evaluate the current design matrix with just the few main factors you determined to be significant, use DOE>Design Diagnostics>Evaluate Design. Select only the statistically significant factors for the evaluation. Look at the Alias Matrix to see what the problems are with using the same 20 runs to estimate the interaction effects (confounding of main effects and interaction effects). Specifically, we are interested in the 2-factor interaction between the biggest effects. What main factors are confounded with this interaction and what is the magnitude? Interpret the finding. (Note: find the column of the 2-factor interaction which had the largest effect. Then see what row has a number different from zero and what the main effect in that row is. The larger the absolute value the larger is the confounding. )4. Now we want to evaluate the data based on our discovery that the 2-factor interaction is confounded with another important factor. Go back to the open window you had before (DOE>Classical>Two Level Screening> Fit Two Level Screening ) and select the statistically significant factors plus the 2-factor interaction of the two biggest effects. Click Run Model again. Interpret the output. What is likely happening?5. Make a final selection on the window (DOE>Classical>Two Level Screening> Fit Two Level Screening) of what you think is the true likely factors and or interactions. Then click Run Model again. Interpret final model. Prepare the report using the following formatting guidelines:1 page, single-spaced report using 0.5 margins and two-column format1 page for appendixInclude title of report, then FirstName, LastName, ISDS course #, Assignment #, date (00/00/00)10 pt Font Calibri or Times New RomanJustified as sample reportCreate headings for each sectionList any references used (e.g. Module 1 Resources)Include a title for your report e.g. "Text Analysis of Workers Compensation Claims" and create headings for each sectionInclude supporting relevant figures from the analysis in your AppendixSubmit as pdf with filename first name initial last name and assignment number (for instance HSchneider#1)Be sure to review the Assignment Rubric and Assignment Example attached below. If you have any questions, please post in the Module Questions Forum.