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5. Suppose that we have f(x)e. Use derivatives to answer the following questions. Solutions based on graphical or numerical work will receive no credit. (a) (4pts) Find f"(), the second deriv...
Let f(x,y) = 4 + x² + y² – 3xy f has critical points at 10,0)...
Let f(x,y) = 4 + x² + y² – 3xy f has critical points at 10,0) and (1,1) use the second derivative test to classify these points as local min, local max, or saddle point
Find the critical points of the following function. Use the Second Derivative Test to determine if...
Find the critical points of the following function. Use the Second Derivative Test to determine if possible) whether each critical point corresponds to a local maximum, local minimum or saddle point. Contem your results with a graphing utility f(x,y) = x + xy-2) + 4y - 12 What are the critical points? (Type an ordered pair Use a comma to separate answers as needed.) Use the Second Derivative Test to find the local maxima. Select the correct choice below and,...
(1 point) Find the critical points of f(x) and use the Second Derivative Test of possible)...
(1 point) Find the critical points of f(x) and use the Second Derivative Test of possible) to determine whether each corresponds to a local minimum or maximum. Let f(x) = x exp(-x) e lest ? Critical Point 1 - Critical Point 2 - is what by the Second Derivative Test? is what by the Second Derivative Test?
1. (25 points) The figure below shows the contour plot of f(x,y)-3 -1 - 2y+y. (Credit for the figure is due to UMich instructors.) 6.00U 6.000 1.5 1.0 0.5 0.0 0.5 1.0 1.5 6.000 2.0-1.5-1.0-0.5 0.0 0....
1. (25 points) The figure below shows the contour plot of f(x,y)-3 -1 - 2y+y. (Credit for the figure is due to UMich instructors.) 6.00U 6.000 1.5 1.0 0.5 0.0 0.5 1.0 1.5 6.000 2.0-1.5-1.0-0.5 0.0 0.5 1.0 1.5 (a) Find all critical points of f. There should be six. Mark them on the contour plot. (Think, but don't write, about how to guess the critical points from the contour plot.) (b) Find f-,) v(,),and fp()-fy(, y) (c) Try to...
Question 6. (20 pts) Find the critical points of f(x, y) = x4 + 2y2 –...
Question 6. (20 pts) Find the critical points of f(x, y) = x4 + 2y2 – 4xy. Then use the Second Derivative Test to determine whether each critical point is a local min, max, or saddle point.
1. (12 points) Find all the critical points of f(x) = (x - 1)(x + 5)...
1. (12 points) Find all the critical points of f(x) = (x - 1)(x + 5) Hint: Do not expand! Instead use the product and chain rules then factor 2. (12 points) Find the absolute extrema of f(x) = on (-1,2). Give your answers as (x,y) points. Hint: It is much easier to take the derivative of f(x) by rewriting as f(x) = (1 + x4)-1 and use the chain rule 3. f(x) = ? - 7x + 1 (a)...
1. Find the critical point of f(x) = (x + 1)". 2. Use the Second Derivative...
1. Find the critical point of f(x) = (x + 1)". 2. Use the Second Derivative Test to determine whether f(x) = (x + 1)" has a local maximum or a local minimum at x = 0
#1,2,4,5,7 Chapter 4 Functions of Two Variables Applied Calculus 272 4.3 Exercises For problems 1 through 6, find f/, f, and f, for the function given. Confirm that ух 3. f(t,y)-Sxy 4. f(x, y)-e&#...
#1,2,4,5,7
Chapter 4 Functions of Two Variables Applied Calculus 272 4.3 Exercises For problems 1 through 6, find f/, f, and f, for the function given. Confirm that ух 3. f(t,y)-Sxy 4. f(x, y)-e" 5.(x,y)-In(axy+2x-6y) y4-5 7. Find the critical points of f(x,y)-ys_x3 + 15x2-12y+12 and use the Second Derivative Test to classify them. If the test fails, say "the test fails. 3
Chapter 4 Functions of Two Variables Applied Calculus 272 4.3 Exercises For problems 1 through 6, find...
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,...
Show ALL work to receive rating. Thanks! 1. Let f(x) = -4x^3+6x^2 a) Where is f(x)...
Show ALL work to receive rating. Thanks! 1. Let f(x) = -4x^3+6x^2 a) Where is f(x) increasing/decreasing? Make a sign chart. b) Classify the critical points as local max, local min, or neither. c) Where is f(x) concave up/concave down? Does it have any points of inflection? d) Use the information above to sketch the curve. Note that f(1/2) = 1. Be sure your graph includes the x and y intercepts if they exist.
Let f(x,y) = 4 + x² + y² – 3xy f has critical points at 10,0) and (1,1) use the second derivative test to classify these points as local min, local max, or saddle point
Find the critical points of the following function. Use the Second Derivative Test to determine if possible) whether each critical point corresponds to a local maximum, local minimum or saddle point. Contem your results with a graphing utility f(x,y) = x + xy-2) + 4y - 12 What are the critical points? (Type an ordered pair Use a comma to separate answers as needed.) Use the Second Derivative Test to find the local maxima. Select the correct choice below and,...
(1 point) Find the critical points of f(x) and use the Second Derivative Test of possible) to determine whether each corresponds to a local minimum or maximum. Let f(x) = x exp(-x) e lest ? Critical Point 1 - Critical Point 2 - is what by the Second Derivative Test? is what by the Second Derivative Test?
1. (25 points) The figure below shows the contour plot of f(x,y)-3 -1 - 2y+y. (Credit for the figure is due to UMich instructors.) 6.00U 6.000 1.5 1.0 0.5 0.0 0.5 1.0 1.5 6.000 2.0-1.5-1.0-0.5 0.0 0.5 1.0 1.5 (a) Find all critical points of f. There should be six. Mark them on the contour plot. (Think, but don't write, about how to guess the critical points from the contour plot.) (b) Find f-,) v(,),and fp()-fy(, y) (c) Try to...
Question 6. (20 pts) Find the critical points of f(x, y) = x4 + 2y2 – 4xy. Then use the Second Derivative Test to determine whether each critical point is a local min, max, or saddle point.
1. (12 points) Find all the critical points of f(x) = (x - 1)(x + 5) Hint: Do not expand! Instead use the product and chain rules then factor 2. (12 points) Find the absolute extrema of f(x) = on (-1,2). Give your answers as (x,y) points. Hint: It is much easier to take the derivative of f(x) by rewriting as f(x) = (1 + x4)-1 and use the chain rule 3. f(x) = ? - 7x + 1 (a)...
1. Find the critical point of f(x) = (x + 1)". 2. Use the Second Derivative Test to determine whether f(x) = (x + 1)" has a local maximum or a local minimum at x = 0
#1,2,4,5,7
Chapter 4 Functions of Two Variables Applied Calculus 272 4.3 Exercises For problems 1 through 6, find f/, f, and f, for the function given. Confirm that ух 3. f(t,y)-Sxy 4. f(x, y)-e" 5.(x,y)-In(axy+2x-6y) y4-5 7. Find the critical points of f(x,y)-ys_x3 + 15x2-12y+12 and use the Second Derivative Test to classify them. If the test fails, say "the test fails. 3
Chapter 4 Functions of Two Variables Applied Calculus 272 4.3 Exercises For problems 1 through 6, find...
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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