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You are a researcher in a large lab with an unlimited budget. Because of all of your money, you have the flexibility to choose different techniques to answer important questions. You have several collaborators interested in exploring the relationship between different brain regions and behaviors of interest and have tasked you with designing studies. One of your collaborators is really interested in direct measures of neural activity related to play behaviors. Design a behavioral intervention study that identifies i) a relevant brain region ii) your control and experimental groups, iii) a technique you would use, iv) description of the technique, and the v) question you want to answer with your study. Because of all the extra money you have, your collaborator wants to explore more about play. They want to know how posterior connections to the region identified in part A may impact behavior. Describe i) what view of the brain would help you determine a posterior structure to your region of interest, ii) a brain region that is posterior to your region of interest from A, iii) a technique that could manipulate neural activity in your new region of interest, and iv) a description of how you would use that technique to either test necessity or sufficiency.

The password for your online exam is: lakeviewThe link for the online exam is in the Step 1 folder and you should have opened it in a new tab before you begin this test.Instructions:Before you begin your exam, hold up all sheets of paper you will be using to the camera to show that there is nothing written on it. Formula sheet is available  below Question 1.Enter the password found above into the online exam tab open in Step 1 and complete the exam. Once completed, hold up each completed sheet of paper to the camera.Answer the Yes/No question below and proceed to the next question.DO NOT SUBMIT OR CLOSE YOUR TEST before answering all the questions.Question:I have completed and submitted my online exam and I have held up all my sheets of paper (front and back) to record an image of them on the camera.

Solve the initial value problem.  =   + 3, y(9) = 1

Find the largest open intervals where the function is concave upward.f(x) = x 3 – 6x 2 – 7x + 51

Use implicit differentiation to find dy/dx and d2y/dx2.y 2 – x 2 = 3

Provide an appropriate response.Suppose the derivative of the function y = f(x) is y’ = (x – 5) 2(x + 9). At what points, if any, does the graph of f have a local minimum or local maximum?

Find an equation for the tangent to the curve at the given point.h(x) = t 3 – 16t – 5, (4, -5)

Evaluate the definite integral. dt

At the given point, find the slope of the curve, the line that is tangent to the curve, or the line that is normal to the curve, as requested.y 5 + x 3 = y 2 + 9x, tangent at (0, 1)

Use the substitution formula to evaluate the integral. dx