Question

the function x^8 + y^8 has a critical point at (0,0). What
sort of critical point is it?

Answer #1

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 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 of the function
f(x,y)=-6-7x+x^2+8y-7y^2
This critical point is a ?

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 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))

let g(x) be a continuous function that has exactly one critical
point in the interval(-12,-8)
find the x values at which the global maximum and the global
minimum occur in this interval given that
g'(-8)=0 and g''(-8)=4
global maximum at x=
global minimum at x=

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) 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 Derivative Test to determine whether it is
A. a local minimum
B. a local maximum
C. test fails
D. a saddle point

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 23 minutes ago

asked 32 minutes ago

asked 32 minutes ago

asked 46 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 2 hours ago