Find the maximum and minimum values of the given function

Reference no: EM131012986

Let f(x,y) = x³ - 12xy + 8y³.

a. Find the following quantities

i. f_x =
ii. f_y =
iii. f_xx =
iv. f_xy =
v. f_yy =

b. Solve f_x = 0, f_y = 0 for critical point (x, y).

c. Use the second derivative test to determine the critical points in (b) are local maximum oi minimum or saddle points.

2. Use Lagrange multipliers to find the maximum and minimum values of the function f(x,y,z) = 2x + 2y+ z subject to x² + y² +z² = 9.

Reference no: EM131012986

Questions Cloud

The partnership was formed : Zinc, LP was formed on August 1, 20X9. When the partnership was formed, Al contributed $10,000 in cash and inventory with a FMV and tax basis of $40,000. In addition, Bill contributed equipment with a FMV of $30,000 and adjusted basis of $25,000 alon..

How you got the answer for this questionassume alpha : 240,000Common Stock, $10 Par Value, 100,000 shares authorized, 50,000 shares issued and outstanding500,000Additional Paid In Capital ½ Common Stock

How does your background impact your values on punishment : What forms/types of punishment do you believe would be most effective to achieve the type of behavior you want from your children?

Determine the horizontal deflection of joint c : Each member of the truss shown is made of steel (Est = 200GPa) and has the cross- sectional area shown. If the applied load P on point E is 40 kN, determine the vertical deflection of joint C by using Castiglione's second theorem.

Find the maximum and minimum values of the given function : Use Lagrange multipliers to find the maximum and minimum values of the function f(x,y,z) = 2x + 2y+ z subject to x2 + y2 +z2 = 9.

Prepare a classified balance sheet - review of the basics : Analyze transactions in a worksheet. At the end, you should have balances for the 1/31/2016 balance sheet and income statement. Set up a separate column for each balance sheet and income statement account affected.

Does the confidence interval contain the value of four years : Does the confidence interval contain the value of 4 years? Is there anything about the data that would suggest that the confidence interval might not be a good result

Calculate the effective revenue with the hedge : Compute gain or loss in the futures market after describing the transactions. Calculate the effective revenue with the hedge. Describe all transactions clearly.

At what time is the paper clip at its maximum height : Let s(t) = 64t - 2t2 represent the height in feet of a paper clip that is shot straight up in the air with a rubber band where t is in seconds. At what time is the paper clip at its maximum height

User Account

All Pages