b WeBWork England MAT x C Essential Calculus Early Tri X Account Summary Bb Blac

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b WeBWork England MAT x C Essential Calculus Early Tri X Account Summary Bb Blackboard Learn C https://webwork.asu.edu MAT 267 Spring 2015 Section 7/3/ /webwork2/England Problem 6 least one of the answe above NOT correct Problem 7 3 of the questions remain unanswered. Problem 8 (1 pt) ch of the following functions has at most one critical point. Graph a few level curves and a few gradiants and, on this basis alone, Problem 9 Problem 10 decide whether the critical point is a local maximum (MA), a local minimum (M or a saddle point (S). Enter the appropriate abbreviation for Problem 11 each question, or N if there is no critical point. Problem 12 A) f(z, y) Problem 13 Type of critical point: Problem 14 Problem 15 B) f(z, y) Problem 16 Type of critical point: Display options Type of critical point: MI View equations as: Images Math Jax Type of critical point: Show saved answers? Yes No Note: You can earn partial credit on this problem. Use Equation Editor? Yes Preview Answers Submit Answers No Your score was recorded Apply options You have attempted this problem 2 times. You received a score of 25% for this attempt. Your overall recorded score is 25%. You have 2 attempts remaining. 1 PM 3/9/2015

Explanation / Answer

A) F = e^(-2x^2 - 4y^2)

Fx = e^(-2x^2 - 4y^2) * (-4x) = 0 ---> -4x = 0 ---> x = 0

Fy = e^(-2x^2 - 4y^2) * (-8y) ---> -8y = 0 ---> y = 0

So, the critical point is (0 , 0)

And it is a local maximum, MA

B)

F = e^(2x^2 - 4y^2)

Fx = e^(2x^2 - 4y^2) * 4x) --> 4x = 0 ---> x = 0

Fy = e^(2x^2 - 4y^2) * (-8y) --> -8y = 0 ---> y = 0

So, the critical point is (0, 0)

And it is a local maximum, MA

C)

F = 2x^2 + 4y^2 + 2

Fx = 4x = 0 --> x = 0

Fy = 8y = 0 --> y = 0

So, critical point is (0 , 0)

And it is a local minimum, MI

D)

F = 2x + 4y + 2

Fx = 2 = 0 ---> no solution for x

Fy = 4 = 0 ---> no solution for y

So, no critical points

So, enter N

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