Question

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*

Answer #1

Let f(x,y) = 3x^2y − 2y^2 − 3x^2 − 8y + 2.
(i) Find the stationary points of f.
(ii) For each stationary point P found in (i), determine whether
f has a local maximum, a local minimum, or a saddle point at P.
Answer:
(i) (0, −2), (2, 1), (−2, 1)
(ii) (0, −2) loc. max, (± 2, 1) saddle points

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).

2. Consider the function f(x, y) = x 2 + cos(πy). (a) Find all
the Critical Points of f and (b) Classify them as local
maximum/minimum or neither

Find all local maximum or local minimum or saddle point for f(x,y)=
8y^3 + 12x^2 -24xy

Find the location of the critical point of the function
f(x,y)= kx^(2)+3y^(2)-2xy-24y (in terms of k) of
t. The classify the values of k for which the critical
point is a:
I) Saddle Point
II) Local Minimum
III) Local Maximum

Consider the function below. y=f(x)= x/x^2+x+1
Find all critical numbers of (f), if any.
Find interval(s) on which f is decreasing
Final all local maximum/minimum points of f.

If f(x,y)=(5∗x3+4∗y3+4∗x∗y+1) find the critical point for
f(x,y)
x=____
y=____
Is this critical point a local maximum, local minimum, or saddle
point?

Consider the following function. g(x, y) = e− 4x^2 + 4y^2 + 8
√ 8y (a) Find the critical point of g. If the critical point is
(a, b) then enter 'a,b' (without the quotes) into the answer box.
(b) Using your critical point in (a), find the value of D(a, b)
from the Second Partials test that is used to classify the critical
point. (c) Use the Second Partials test to classify the critical
point from (a).
A) Saddle...

Given the function f (x, y) = ax^2
2 + 2xy + ay.y
2-ax-ay. Take
for a an integer value that is either greater than 1 or less
than -1, and
then determine the critical point of this function. Then
indicate whether it is
is a local maximum, a local minimum or a saddle point.
Given the function f (x, y) = ax^2 +2 + 2xy + ay^2-2-ax-ay.
Take
for a an integer value that is either greater than 1...

For the questions below, consider the following function.
f (x) = 3x^4 - 8x^3 + 6x^2
(a) Find the critical point(s) of f.
(b) Determine the intervals on which f is increasing or
decreasing.
(c) Determine the intervals on which f is concave up or concave
down.
(d) Determine whether each critical point is a local maximum, a
local minimum, or neither.

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