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Find the local extrema of the function: g ( x ) = x 2 e − x 2 {“version”:”1.1″,”math”:”g(x)=x^2 e^{-x^2}”} State your answers as points and label them as maxima or minima respectively. Select an option from below:

The figure shows the graph of the derivative, f'(x), of a function f(x). Answer the following questions and explain your reasoning. (a) For what values of x does f(x) have a local maximum and/or local minimum?(b) Sketch a graph of f”(x).(c) Sketch a possible graph of f(x) Select an option from below:

Choose one of the following three optimization problems. Pay attention to the points. (a) For 8 points.The ideal dosage of a medication is a tradeoff between the efficacy of the drug and the severity of its side effects. If the side effects of a treatment are too severe, it will have to be discontinued, so it will fail to treat the patient. Similarly, if the dosage of the medicine is too low, its efficacy will not be sufficient to treat the patient. Suppose the probability of an effective treatment that accounts for this tradeoff is given by P(x), given below, where $x$ is the dosage of the medication given to the patient. What is the ideal dosage to maximize the cure?  P ( x ) = x 1 + x {“version”:”1.1″,”math”:”P(x)=\dfrac{\sqrt{x}}{1+x}”} (b) For 10 points.A box with an open top is to be constructed from a rectangular piece of cardboard (5 ft wide and 8 ft long) by cutting out a square from each of the four corners and bending up the sides. Find the largest volume that such a box can have. (c) For 12 points.An action movie character that loves to break the fourth wall is escaping from a mob of doppelgangers that want to take his place in the movie. He reaches a bank of a straight river, 3 km wide, with a boat unsuspiciously waiting for him. On the other side of the bank, 8 km downstream, he sees The Rock waving at him ready to fly a helicopter for their escape. At this moment he looks directly at the camera (at you) and asks “How can I move the fastest?” while getting himself on the boat. You know he can row at a speed of 6 km/hr and he can run at a speed of 8 km/hr. Should he go directly across (from A to C) and run the rest of the way (to B)? Should he row directly to the helicopter (from A to B)? or should he row for a bit (from A to D) and then run all that’s left to the helicopter? How long will it take him to reach the rock in the shortest time? He’s still staring at the camera, but the sound of the mob is getting louder, he’s counting on you! Select an option from below:

This exam is worth 100 points. It consists of writing several MongoDB queries and MongoDB tools commands. The submitted JS file must run in order to be graded. If one of your queries does not work you should comment out the query so the rest of your queries run. No credit will be given if the .js file does not run with mongosh. This is an individual assignment. You MAY NOT consult with other students. The only allowed references are:  MongoDB documentation: https://www.mongodb.com/docs/ The regex “cheat sheet” on myCourses Crib sheet: 8½” x 11″ (A4), hand-written, double-sided You may not access any files that you or anyone else have written for this course. Download the practical starter files from here: mongo_practical_start_610.zip Rename the JS starter file to practical_YourName.js before beginning. When you’re done, be sure to zip your file before uploading the file below.   Load the provided exam_tweets.json into a collection named “Tweets” in a database named “ExamSocial” using mongoimport. Paste the command into the comment in the JS file.  Insert a document with the following information into the Tweets collection. fromUser: your RIT username; for example: abc1234 fromUserName: your name here text: “Semester of Mongo 2025!”Show the results of the insert (i.e., the JSON object with “acknowledged: true”). Write a query that selects the document you entered above using the fromUser field. Project only the fromUser, fromUserName, and text fields. Write a query that updates the text field in the above document to say:”And now on to Neo4j!”.Do not update the other fields in the document. Show the results of the update (i.e., the JSON object with “acknowledged: true”). Repeat query #3 here to see if the update worked (copy/paste #3). Write a query that will delete the document you added in #2 above using the fromUser field for selection. Show the results from the deletion (i.e., the JSON object with “acknowledged: true”). Using regular expressions similar to what we have done in class, select all the documents that contain both of the two following words in the text field: “great” – the full word; no stem words – it should not find “greatness” “not” – the full word; no stem words – it should not find “knot”The words can be in either order in the document.Both words should be complete words with no prefix of suffix (additional letters).The search should be case insensitive.Show only the _id and text fields in your results. This question is about using GridFS: Using mongofiles on the OS command line, take the sandy.png file and insert it into the ExamSocial database. Paste the command you used into the corresponding comment in the JS file. Write a query that selects everything from the fs.files document that was created when you ran mongofiles. For all documents in the collection, add a new property called tweetLoc whose value is a GeoJSON point built from latitude and longitude. Do not delete the latitude and longitude properties. Show the results from the update. Add an index to the new tweetLoc property to support GeoSpatial queries. Show the results from adding the index. Write a geospatial query to find the tweet that’s within 50km of: latitude: 36 longitude: -115Project only the text, latitude, and longitude fields. Once you are done with the exam, zip up your JS file and attach it here with the “Add a file” button below. You don’t need to type anything into the text area response field.

[FinA] A major problem with the typical portrayal in the media of very young children as “Gerber babies” is that these images may:

[FinA] Of the behaviors listed below, which is likely to be the most important (and common) target for developing a prescriptive pediatric behavioral treatment for a toddler?

[FinA] Since her head injury, Olivia has become less courteous and frequently uses profanity, a stark contrast to her previous considerate nature. Her friends have noticed these significant changes. Which type of injury is most likely that Olivia has experienced?

[FinA] Renee recently moved into a group residential facility that provides treatment for dementia patients. Renee has stopped interacting with her caregivers and spends most of her time in bed. Which of the following challenging behaviors of dementia is Renee exhibiting?

[FinA] Which scenario describes an individual potentially experiencing a side-effect of an occipital lobe injury?

[FinA] After a consult with the client’s parents, the behavior coach has the client sign an agreement that she will earn the pair of new sneakers she wants if she practices her softball throws every day for two weeks to improve her game.   What strategy is the client and her coach using?