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Problem #10: Consider the following function. 8(x,y) = {2x2 – 3y2 +6V6 y (a) Find the...
Problem #10: Consider the following function. 8(x,y) = 8x? - 7y2 + 16V7x (a) Find the...
Problem #10: Consider the following function. 8(x,y) = 8x? - 7y2 + 16V7x (a) Find the critical point of g. If the critical point is (a, b) then enter a b (without the quotes) into the answer box. (b) Using your critical point in (a), find the value of D(a,b) from the Second Partials test that is used to classify the critical point. (c) Use the Second Partials test to classify the critical point from (a). Problem #10(a): Enter your...
Consider the following function. 8(x,y) = -372 – 8y2 +6V8x (a) Find the critical point of...
Consider the following function. 8(x,y) = -372 – 8y2 +6V8x (a) Find the critical point of 8. If the critical point is (a,b) then enter a,b (without the quotes) into the answer box. (b) Using your critical point in (a), find the value of D(a,b) from the Second Partials test that is used to classify the critical point. (e) Use the Second Partials test to classify the critical point from (a).
5. [-13 Points) DETAILS TANAPCALC10 8.R.029. Consider the following. Ax,y) - 2x2 + y2 - 12x...
5. [-13 Points) DETAILS TANAPCALC10 8.R.029. Consider the following. Ax,y) - 2x2 + y2 - 12x - 4y + 4 Find the critical points of the function. (If an answer does not exist, enter DNE.) (x, y) = Use the second derivative test to classify the nature of each of these points, if possible. O relative maximum relative minimum saddle point inconclusive no critical point Finally, determine the relative extrema of the function. (If an answer does not exist, enter...
2. For the two-argument function defined below: f(x,y) = 2x2 – 8xy + 5y + 3y2...
2. For the two-argument function defined below: f(x,y) = 2x2 – 8xy + 5y + 3y2 (a) Find fx = and fex = . (5 marks) (b) Find fy = and fyy (5 marks) (c) Determine the critical point(s) of the f(x,y). (8 marks) (d) Find fxy (3 marks) (e) Determine each of the critical point(s) in the above (c) whether is a local minimum, local maximum or saddle point by using second partial derivative test. (4 marks)
Find the critical point of the function. Then use the second derivative test to classify the...
Find the critical point of the function. Then use the second derivative test to classify the nature of this point, if possible. (If an answer does not exist, enter DNE.) f(x, y) = x2 − 4xy + 2y2 + 4x + 8y + 8 critical point (x, y)= classification ---Select--- :relative maximum, relative minimum ,saddle point, inconclusive ,no critical points Finally, determine the relative extrema of the function. (If an answer does not exist, enter DNE.) relative minimum value= relative...
Consider the function ?(?, ?) = ?3 + ?2 + 4?? − 2. 1. Find all...
Consider the function ?(?, ?) = ?3 + ?2 + 4?? − 2. 1. Find all critical points of ?. 2. Use the Second Partials Test to determine whether each of the critical points of ? gives a relative maximum, relative minimum, or saddle point. You must clearly demonstrate your use the the Second Partials Test to determine the answer. Write your answers in the blanks below and then provide the specific information that you used to make your determination...
Consider the function G(x,y) = 2x4 + 4xy + 3y2 + 8x Find an expression for...
Consider the function G(x,y) = 2x4 + 4xy + 3y2 + 8x Find an expression for D(x,y), the function that is used to determine if a critical point is an extremum or a saddle point. You do NOT have to find any critical points, only the function D.
Problem 8. (1 point) For the function f(x,y) = 4x² + 6xy + 2y”, find and...
Problem 8. (1 point) For the function f(x,y) = 4x² + 6xy + 2y”, find and classify all critical points. O A. (0,0), Saddle O B. (4,6), Saddle O C. (4,6), Relative Minimum OD. (0,0), Relative Minimum OE. (0,0), Saddle |(4,6), Relative Maximum
2. Let f(x,y) = 2x2 - 6xy + 3y2 be a function defined on xy-plane (a)...
2. Let f(x,y) = 2x2 - 6xy + 3y2 be a function defined on xy-plane (a) Find first and second partial derivatives of (b) Determine the local extreme points off (max., min., saddle points) if there are any. (c) Find the absolute max. and absolute min. values of f over the closed region bounded by the lines x= 1, y = 0, and y = x
please solve all parts. For the function f(x,y)=x3+y3 – 6y2-3x+5, do the following: (a) Determine its...
please solve all parts.
For the function f(x,y)=x3+y3 – 6y2-3x+5, do the following: (a) Determine its critical point(s) if exists. Express your answer as coordinate pairs with parentheses and commas. Separate your answers with commas and list in ascending order of x if the function has more than one critical point. Use **DNE" if the function has no critical point. Answer: (b) Use the D-Test to classify at each critical point whether the function has a relative maximum or minimum,...
Problem #10: Consider the following function. 8(x,y) = 8x? - 7y2 + 16V7x (a) Find the critical point of g. If the critical point is (a, b) then enter a b (without the quotes) into the answer box. (b) Using your critical point in (a), find the value of D(a,b) from the Second Partials test that is used to classify the critical point. (c) Use the Second Partials test to classify the critical point from (a). Problem #10(a): Enter your...
Consider the following function. 8(x,y) = -372 – 8y2 +6V8x (a) Find the critical point of 8. If the critical point is (a,b) then enter a,b (without the quotes) into the answer box. (b) Using your critical point in (a), find the value of D(a,b) from the Second Partials test that is used to classify the critical point. (e) Use the Second Partials test to classify the critical point from (a).
5. [-13 Points) DETAILS TANAPCALC10 8.R.029. Consider the following. Ax,y) - 2x2 + y2 - 12x - 4y + 4 Find the critical points of the function. (If an answer does not exist, enter DNE.) (x, y) = Use the second derivative test to classify the nature of each of these points, if possible. O relative maximum relative minimum saddle point inconclusive no critical point Finally, determine the relative extrema of the function. (If an answer does not exist, enter...
2. For the two-argument function defined below: f(x,y) = 2x2 – 8xy + 5y + 3y2 (a) Find fx = and fex = . (5 marks) (b) Find fy = and fyy (5 marks) (c) Determine the critical point(s) of the f(x,y). (8 marks) (d) Find fxy (3 marks) (e) Determine each of the critical point(s) in the above (c) whether is a local minimum, local maximum or saddle point by using second partial derivative test. (4 marks)
Consider the function G(x,y) = 2x4 + 4xy + 3y2 + 8x Find an expression for D(x,y), the function that is used to determine if a critical point is an extremum or a saddle point. You do NOT have to find any critical points, only the function D.
Problem 8. (1 point) For the function f(x,y) = 4x² + 6xy + 2y”, find and classify all critical points. O A. (0,0), Saddle O B. (4,6), Saddle O C. (4,6), Relative Minimum OD. (0,0), Relative Minimum OE. (0,0), Saddle |(4,6), Relative Maximum
2. Let f(x,y) = 2x2 - 6xy + 3y2 be a function defined on xy-plane (a) Find first and second partial derivatives of (b) Determine the local extreme points off (max., min., saddle points) if there are any. (c) Find the absolute max. and absolute min. values of f over the closed region bounded by the lines x= 1, y = 0, and y = x
please solve all parts.
For the function f(x,y)=x3+y3 – 6y2-3x+5, do the following: (a) Determine its critical point(s) if exists. Express your answer as coordinate pairs with parentheses and commas. Separate your answers with commas and list in ascending order of x if the function has more than one critical point. Use **DNE" if the function has no critical point. Answer: (b) Use the D-Test to classify at each critical point whether the function has a relative maximum or minimum,...
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