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3 2. Find the absolute maximum and minimum values of the function f(x, y) = 4x + 6y = x² - y² on the set: D = {(x, y) : 0 ≤ x, 0

3 2. Find the absolute maximum and minimum values of the function f(x, y) = 4x + 6y = x² - y² on the set: D = {(x, y) : 0 ≤ x, 0

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter4: Calculating The Derivative
Section4.CR: Chapter 4 Review
Problem 3CR: Determine whether each of the following statements is true or false, and explain why. The derivative...
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Can you help me with number 2: finding absolute min and max

X=(1 Math 283, Midterm II November 3, 2022 1. Consider the function: X z = f(x, y) = √√x + e4y (a) Write the equation of the tangent plane to the graph of f at the point P(1,0, √2). 22 (b) Calculate D-f(3,0) where =(,) (c) Is there a direction in which the directional derivative of ƒ at (3,0) has value 1? → Choose ONE of the problems 2 or 3 2. Find the absolute maximum and minimum values of the function f(x, y) = 4x + 6y − x² - y² on the set: 2 D = {(x, y) : 0 ≤ x,0 ≤ y, x² + y² ≤ 25} 3. A space probe in the shape of the ellipsoid 4x² + y² + 4x² = 16 2 Ricardo Ron Pulido enters earth's atmosphere and its surface begins to heat up. After one hour the temperature of the point (x, y, z) on the probes surface is given by the function: 1 T(x, y, z) = 8x² +4yz - 16z+5 Using Lagrange Multiplier method find the hotest and the coolest point on the surface of the probe. 4+201=2
Transcribed Image Text:X=(1 Math 283, Midterm II November 3, 2022 1. Consider the function: X z = f(x, y) = √√x + e4y (a) Write the equation of the tangent plane to the graph of f at the point P(1,0, √2). 22 (b) Calculate D-f(3,0) where =(,) (c) Is there a direction in which the directional derivative of ƒ at (3,0) has value 1? → Choose ONE of the problems 2 or 3 2. Find the absolute maximum and minimum values of the function f(x, y) = 4x + 6y − x² - y² on the set: 2 D = {(x, y) : 0 ≤ x,0 ≤ y, x² + y² ≤ 25} 3. A space probe in the shape of the ellipsoid 4x² + y² + 4x² = 16 2 Ricardo Ron Pulido enters earth's atmosphere and its surface begins to heat up. After one hour the temperature of the point (x, y, z) on the probes surface is given by the function: 1 T(x, y, z) = 8x² +4yz - 16z+5 Using Lagrange Multiplier method find the hotest and the coolest point on the surface of the probe. 4+201=2
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