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10. Let (a, b) be a critical input of z = f(x,y). Which one of the...
Assume that f(x,y) has a continuous partial derivatives and let (1,2) be a critical point. Given...
Assume that f(x,y) has a continuous partial derivatives and let (1,2) be a critical point. Given that far(1,2)=2 fy(1,2), and fx/(1,2)=fyx(1,2)= 18. If f has a saddle point at (1,2), then one of the following statements is true Select one: a. None of the choices is correct answer bif y(1,2) is less than - 3 or greater than 3 c.f xa {1,2) is less than 3 and greater than - 3 d. fxr (1,2) is less than 6 and greater...
Let z equals f left parenthesis x comma y right parenthesis commaz=f(x,y) , where x equals...
Let
z equals f left parenthesis x comma y right parenthesis
commaz=f(x,y) ,
where
x equals u squared plus v squared and y equals StartFraction u
Over v EndFractionx=u2+v2 and y=uv.
Find
StartFraction partial derivative z Over partial derivative u
EndFraction and StartFraction partial derivative z Over partial
derivative v EndFraction∂z∂u and ∂z∂v
at
left parenthesis u comma v right parenthesis equals left
parenthesis negative 6 comma negative 6 right
parenthesis(u,v)=(−6,−6)
,
given that :
f Subscript x Baseline left parenthesis negative 6 comma...
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,...
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)
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
0 Both first partial derivatives of the function f(x,y) are zero at the given points. Use...
0 Both first partial derivatives of the function f(x,y) are zero at the given points. Use the second-derivative test to determine the nature of foxy) at each of these points. If the second-derivative test is inconclusive, so state f(x,y) - 12x² +24xy – 2y + 72y: (-2. - 2) (6.6) What is the nature of the function at (-2. - 2)? A. fxy) has a relative maximum at (-2,-2) B. fxy) has a relative minimum at(-2.-2) OC. XY) has neither...
Question 17 Find and classify the critical point of f (, y) = 263 – 25y?...
Question 17 Find and classify the critical point of f (, y) = 263 – 25y? – 12xy - 11x² + 46y +389. To find the critical point, you must solve two equations. Type them below: Solve this system and round your answers to the hundredths place: Find the third coordinate of the critical point: Calculate the determinant of the second-order partial derivative matrix Fill in each of the remaining spaces with a word or phrase from the following list:...
-n ', S Let f(x,yZFz2_xy. Let v=<1,1,1>. Let point P=<2,1,3> a. Compute gradient of fx,y,z) b....
-n ', S Let f(x,yZFz2_xy. Let v=<1,1,1>. Let point P=<2,1,3> a. Compute gradient of fx,y,z) b. If the contours are far apart, is the length of the gradient large or small? Answer: Explain! What MATLAB command is used to draw the gradient vectors? Answer: - c. Compute the directional derivative in the direction of v. d. Compute the equation of the tangent plane to f(x,y,z) at the point P. e. Use the chain rule to compute r if x t2,...
Problem #7: The graph of z = f (x, y) is shown below. In each part,...
Problem #7:
The graph of z = f (x, y)
is shown below. In each part, determine whether the given partial
derivatives are positive, negative, or zero. (Note that the
function is symmetric about 0 in both the x- and
y- directions.)
(a)
fx(−2, 2) and
fxx(−2, 2)
(b)
fy(−2, 2) and
fyy(−2, 2)
(c)
fx(0, −2) and
fxx(0, −2)
(d)
fy(0, −2) and
fyy(0, −2)
(A) negative, positive (B) negative, zero (C)
positive, negative (D) positive, zero (E) zero, ...
Problem #8: Let f(x, y, z) = xzly. Find the value of the following partial derivatives....
Problem #8: Let f(x, y, z) = xzly. Find the value of the following partial derivatives. (a) fx(4,3,2) (b) fy(4,4,4) (c) fz(3,4,3)
Assume that f(x,y) has a continuous partial derivatives and let (1,2) be a critical point. Given that far(1,2)=2 fy(1,2), and fx/(1,2)=fyx(1,2)= 18. If f has a saddle point at (1,2), then one of the following statements is true Select one: a. None of the choices is correct answer bif y(1,2) is less than - 3 or greater than 3 c.f xa {1,2) is less than 3 and greater than - 3 d. fxr (1,2) is less than 6 and greater...
Let
z equals f left parenthesis x comma y right parenthesis
commaz=f(x,y) ,
where
x equals u squared plus v squared and y equals StartFraction u
Over v EndFractionx=u2+v2 and y=uv.
Find
StartFraction partial derivative z Over partial derivative u
EndFraction and StartFraction partial derivative z Over partial
derivative v EndFraction∂z∂u and ∂z∂v
at
left parenthesis u comma v right parenthesis equals left
parenthesis negative 6 comma negative 6 right
parenthesis(u,v)=(−6,−6)
,
given that :
f Subscript x Baseline left parenthesis negative 6 comma...
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,...
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)
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
0 Both first partial derivatives of the function f(x,y) are zero at the given points. Use the second-derivative test to determine the nature of foxy) at each of these points. If the second-derivative test is inconclusive, so state f(x,y) - 12x² +24xy – 2y + 72y: (-2. - 2) (6.6) What is the nature of the function at (-2. - 2)? A. fxy) has a relative maximum at (-2,-2) B. fxy) has a relative minimum at(-2.-2) OC. XY) has neither...
Question 17 Find and classify the critical point of f (, y) = 263 – 25y? – 12xy - 11x² + 46y +389. To find the critical point, you must solve two equations. Type them below: Solve this system and round your answers to the hundredths place: Find the third coordinate of the critical point: Calculate the determinant of the second-order partial derivative matrix Fill in each of the remaining spaces with a word or phrase from the following list:...
-n ', S Let f(x,yZFz2_xy. Let v=<1,1,1>. Let point P=<2,1,3> a. Compute gradient of fx,y,z) b. If the contours are far apart, is the length of the gradient large or small? Answer: Explain! What MATLAB command is used to draw the gradient vectors? Answer: - c. Compute the directional derivative in the direction of v. d. Compute the equation of the tangent plane to f(x,y,z) at the point P. e. Use the chain rule to compute r if x t2,...
Problem #7:
The graph of z = f (x, y)
is shown below. In each part, determine whether the given partial
derivatives are positive, negative, or zero. (Note that the
function is symmetric about 0 in both the x- and
y- directions.)
(a)
fx(−2, 2) and
fxx(−2, 2)
(b)
fy(−2, 2) and
fyy(−2, 2)
(c)
fx(0, −2) and
fxx(0, −2)
(d)
fy(0, −2) and
fyy(0, −2)
(A) negative, positive (B) negative, zero (C)
positive, negative (D) positive, zero (E) zero, ...
Problem #8: Let f(x, y, z) = xzly. Find the value of the following partial derivatives. (a) fx(4,3,2) (b) fy(4,4,4) (c) fz(3,4,3)
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