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Problem 1. Let f (r, y) 102y5a2-4-4 2y (1) Find and classify the critical points of...
Problem 3: Let f: X -> R, XC R2, be given by f(x, y)n(x 2y 1),...
Problem 3: Let f: X -> R, XC R2, be given by f(x, y)n(x 2y 1), V(r,y) e X Find the maximal domain X and write the second-order Taylor polynomial for f around the point (2,1) E X. (6 points)
Problem 3: Let f: X -> R, XC R2, be given by f(x, y)n(x 2y 1), V(r,y) e X Find the maximal domain X and write the second-order Taylor polynomial for f around the point (2,1) E X. (6 points)
Problem 7. [13 points; 4, 4, 5.] Consider the function f(r, y) 2y ln(r- ). (i) Find the unit direction of steepest incr...
Problem 7. [13 points; 4, 4, 5.] Consider the function f(r, y) 2y ln(r- ). (i) Find the unit direction of steepest increase for f at the point P (2, 1) (ii) Find the directional derivative of f at the point P(2,1) in the direction u = S (iii) Linearly approximate the value f((2,1)00)
Problem 7. [13 points; 4, 4, 5.] Consider the function f(r, y) 2y ln(r- ). (i) Find the unit direction of steepest increase for f at...
(17) Consider the function f that is given by f(x, y)-2y +e Find all its critical points and classify each one as a local maximum, local minimum, or saddle point (17) Consider the function f tha...
(17) Consider the function f that is given by f(x, y)-2y +e Find all its critical points and classify each one as a local maximum, local minimum, or saddle point
(17) Consider the function f that is given by f(x, y)-2y +e Find all its critical points and classify each one as a local maximum, local minimum, or saddle point
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
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
9y3 + 3x2y-6y + 2 . 3. Find and classify all the critical points of f(x,y) 9y3 + 3x2y-6y + 2 . 3. Find and classify all the critical points of f(x,y)
9y3 + 3x2y-6y + 2 . 3. Find and classify all the critical points of f(x,y)
9y3 + 3x2y-6y + 2 . 3. Find and classify all the critical points of f(x,y)
4. Let f(x, y) = 2 - 2x – y + xy. (a) Find the directional...
4. Let f(x, y) = 2 - 2x – y + xy. (a) Find the directional derivative of f at the point (2,1) in the direction (-1,1). [2] (b) Find all the critical points of the function f and classify them as local extrema, saddle points, etc. [2]
5. Let f(x,y) = 3x2 y - y3 - 6x. (a) Find all the critical points...
5. Let f(x,y) = 3x2 y - y3 - 6x. (a) Find all the critical points off. (b) Classify each of the critical points; that is, what type are they? (c) For the same function f(x,y), find the maximum value of f on the unit square, 0 SX S1,0 <y s 1.
Let f(x,y)=1+x2−cos(5y). Find all critical points and classify them as local maxima, local minima, saddle points, or non...
Let f(x,y)=1+x2−cos(5y). Find all critical points and classify them as local maxima, local minima, saddle points, or none of these.
(a) Find and classify all of the critical points of the function X f(x, y, z)...
(a) Find and classify all of the critical points of the function X f(x, y, z) = (x2 +42 + x2)3/2 on the unit sphere. (b) Find and classify all of the critical points of the function f(x, y, z) = x sin(x2 + y2 +22) on the sphere of radius
Problem 3: Let f: X -> R, XC R2, be given by f(x, y)n(x 2y 1), V(r,y) e X Find the maximal domain X and write the second-order Taylor polynomial for f around the point (2,1) E X. (6 points)
Problem 3: Let f: X -> R, XC R2, be given by f(x, y)n(x 2y 1), V(r,y) e X Find the maximal domain X and write the second-order Taylor polynomial for f around the point (2,1) E X. (6 points)
Problem 7. [13 points; 4, 4, 5.] Consider the function f(r, y) 2y ln(r- ). (i) Find the unit direction of steepest increase for f at the point P (2, 1) (ii) Find the directional derivative of f at the point P(2,1) in the direction u = S (iii) Linearly approximate the value f((2,1)00)
Problem 7. [13 points; 4, 4, 5.] Consider the function f(r, y) 2y ln(r- ). (i) Find the unit direction of steepest increase for f at...
(17) Consider the function f that is given by f(x, y)-2y +e Find all its critical points and classify each one as a local maximum, local minimum, or saddle point
(17) Consider the function f that is given by f(x, y)-2y +e Find all its critical points and classify each one as a local maximum, local minimum, or saddle point
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
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
9y3 + 3x2y-6y + 2 . 3. Find and classify all the critical points of f(x,y)
9y3 + 3x2y-6y + 2 . 3. Find and classify all the critical points of f(x,y)
4. Let f(x, y) = 2 - 2x – y + xy. (a) Find the directional derivative of f at the point (2,1) in the direction (-1,1). [2] (b) Find all the critical points of the function f and classify them as local extrema, saddle points, etc. [2]
5. Let f(x,y) = 3x2 y - y3 - 6x. (a) Find all the critical points off. (b) Classify each of the critical points; that is, what type are they? (c) For the same function f(x,y), find the maximum value of f on the unit square, 0 SX S1,0 <y s 1.
(a) Find and classify all of the critical points of the function X f(x, y, z) = (x2 +42 + x2)3/2 on the unit sphere. (b) Find and classify all of the critical points of the function f(x, y, z) = x sin(x2 + y2 +22) on the sphere of radius
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