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Partial derivative and double integral

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The problems are attached

1 -5 based on Chapter Partial Derivative - (Maximum & Minimum Values and Lagrange Multipliers

1. Locate all relative maxima, relative minima, and saddle points of the surface defined by the following function.

2. Consider the minimization of
subject to the constraint of

(a) Draw the constraint curve on top of with y-axis
and x-axis between -2 and 6. Estimate where extrema values may occur and
compute the function values corresponding to these extrema.

(b) Solve the problem in part (a) with the aid Lagrange multipliers. You may
have to solve the equations numerically. Compare your answers with those in
the part (a).

3. Let represent the temperature at
each of the sphere . Find the maximum
temperature on the curve formed by the intersection of the sphere and the

Apply the method of Lagrange multipliers with two constraints. That is, maximize
where and where

4. Find the absolute extrema of the following function on the indicated closed and bounded set R.

5. An international organization must decide how to spend the $2000 they have been
allotted for famine relief in a remote area. They expect to divide the money between buying rice at $5/sack and beans at $10/sack. The number, P, people who would be fed if they buy x sacks of rice and y sacks of beans is given by

See attachments for proper equations and questions

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Solution Summary

This shows how to find maxima and minima.

Solution provided by:
  • BSc , Wuhan Univ. China
  • MA, Shandong Univ.
Recent Feedback
  • "Your solution, looks excellent. I recognize things from previous chapters. I have seen the standard deviation formula you used to get 5.154. I do understand the Central Limit Theorem needs the sample size (n) to be greater than 30, we have 100. I do understand the sample mean(s) of the population will follow a normal distribution, and that CLT states the sample mean of population is the population (mean), we have 143.74. But when and WHY do we use the standard deviation formula where you got 5.154. WHEN & Why use standard deviation of the sample mean. I don't understand, why don't we simply use the "100" I understand that standard deviation is the square root of variance. I do understand that the variance is the square of the differences of each sample data value minus the mean. But somehow, why not use 100, why use standard deviation of sample mean? Please help explain."
  • "excellent work"
  • "Thank you so much for all of your help!!! I will be posting another assignment. Please let me know (once posted), if the credits I'm offering is enough or you ! Thanks again!"
  • "Thank you"
  • "Thank you very much for your valuable time and assistance!"
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