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Parts (a), (b) are distinct from each other. (a) Find and classify the critical points of the function \(f(x,y)=xy \ e^{-x-y}\). (i.e. local maxima, local minima and saddle points.)   (b)  Find the maximum and minimum values of \(g(x,y)=xy-8x-y^2+y+2\) over the closed triangular region with vertices (0,0), (3,0) and (0,3).   PLEASE READ THE INSTRUCTIONS BELOW CAREFULLY: When you have completed your entire exam do not hit “Submit” to submit the exam on Canvas yet, get your phone and scan your written work for questions 6, 7 and 8 (only) to upload to Gradescope www.gradescope.com or use the gradescope app. Make sure that all pages have been uploaded to Gradescope. Once you’re done scanning and uploading to Gradescope, then submit the exam on Canvas. If you experience any difficulties uploading your solutions to Gradescope, only then submit a single .pdf file in the space provided below. Do not close the current Honorlock session until you have submitted your solutions to Gradescope and then submitted the exam on Canvas. Submitting any solutions to Gradescope or Canvas after the Honorlock proctoring session has ended constitutes a violation of the UMass Academic Honesty policy and will be dealt with accordingly.

A vector function \(\vec{r}(t)\) representing the curve of intersection between the cylinder \(x^2+y^2=1\) and the curve \(z=2x^2y\) is given by:

For questions 1-5, there is no partial credit awarded and it is not necessary to show your work. For those questions, only answers submitted through Canvas will be accepted. Traces of the surface \(1+\dfrac{z^2}{9}=\dfrac{x^2}{4}-\dfrac{y^2}{25}\) are:

Find the value of \(k\) for which the four points \(A(1,7,-2)\), \(B(3,5,6)\), \(C(-1,6,-4)\) and \(D(-4,-3,k)\) all lie on the same plane. \(k\)=.

Assess which of the following statements best describes outsourcing in the pharmaceutical industry?

Which of the following statements correctly describes GMP requirements for documentation?

During the manufacturing of a sterile injectable, a filter shows a small defect. No contaminated batches have been detected yet. At what point does this defect (hazard) become a risk?                                                                                                                                  

During the manufacturing of a sterile injectable, a filter shows a small defect. No contaminated batches have been detected yet. At what point does this defect (hazard) become a risk?                                                                                                                                  

What are the minimum elements a logbook should contain according to GMP?                                                                                                                                        

A newly drafted SOP contains long paragraphs, overly technical language, and some steps written as suggestions (using “may” instead of “must”). Which of the following indicate non-compliance with good documentation practices? (Select all that apply.)