You are given that the function f(x,y)=8x2+y2+2x2y+3 has first
partials fx(x,y)=16x+4xy and fy(x,y)=2y+2x2, and has second...
You are given that the function f(x,y)=8x2+y2+2x2y+3 has first
partials fx(x,y)=16x+4xy and fy(x,y)=2y+2x2, and has second
partials fxx(x,y)=16+4y, fxy(x,y)=4x and fyy(x,y)=2. Consider the
point (0,0). Which one of the following statements is true?
A. (0,0) is not a critical point of f(x,y).
B. f(x,y) has a saddle point at (0,0).
C. f(x,y) has a local maximum at (0,0).
D. f(x,y) has a local minimum at (0,0).
E. The second derivative test provides no information about the
behaviour of f(x,y) at...
Is the function f(x,y)=x−yx+y continuous at the point (−1,−1)?
If not, why is the function not...
Is the function f(x,y)=x−yx+y continuous at the point (−1,−1)?
If not, why is the function not continuous?
Select the correct answer below:
A. Yes
B. No, because lim(x,y)→(−1,1)x−yx+y=−1 and f(0,0)=0.
C. No, because lim(x,y)→(−1,1)x−yx+y does not exist and f(0,0)
does not exist.
D. No, because lim(x,y)→(0,0)x2−y2x2+y2=1 and f(0,0)=0.
Find the Critical point(s) of the function f(x, y) = x^2 + y^2 +
xy -...
Find the Critical point(s) of the function f(x, y) = x^2 + y^2 +
xy - 3x - 5. Then determine whether each critical point is a local
maximum, local minimum, or saddle point. Then find the value of the
function at the extreme(s).
Consider the function f(x,y) = -8x^2-8y^2+x+y
Select all that apply:
1. The function has two critical...
Consider the function f(x,y) = -8x^2-8y^2+x+y
Select all that apply:
1. The function has two critical points
2. The function has a saddle point
3. The function has a local maximum
4. The function has a local minimum
5. The function has one critical point
*Please show your work so I can follow along*
find the limit, if it exists
Lim (x,y)=(0,0) (xy^4)/((x^2)+(y^8))
find the limit, if it exists
Lim (x,y)=(0,0) (xy^4)/((x^2)+(y^8))
Prove that the function f(x,y) is differentiable at (0,0) by
using epsilon-delta method.
(1) f(x,y) =...
Prove that the function f(x,y) is differentiable at (0,0) by
using epsilon-delta method.
(1) f(x,y) = x+y+xy
(2) f(x,y) = sin(xy)
Consider the curve given by the equation
sin(?−?)=2?+?sin(x−y)=2x+y. The equation defines ?y as a function
?(?)y(x)...
Consider the curve given by the equation
sin(?−?)=2?+?sin(x−y)=2x+y. The equation defines ?y as a function
?(?)y(x) near (0,0)(0,0).
(a) Find the equation of the tangent line to this curve at the
point (0,0)(0,0).
(b) Find ?″(0)y″(0).
Problem 1.
(1 point)
Find the critical point of the function
f(x,y)=−(6x+y2+ln(|x+y|))f(x,y)=−(6x+y2+ln(|x+y|)).
c=?
Use the Second...
Problem 1.
(1 point)
Find the critical point of the function
f(x,y)=−(6x+y2+ln(|x+y|))f(x,y)=−(6x+y2+ln(|x+y|)).
c=?
Use the Second Derivative Test to determine whether it is
A. a local minimum
B. a local maximum
C. test fails
D. a saddle point