Question

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

Answer #1

Let f(x, y) = (2y-x^2)(y-2x^2) a. Show that f(x, y) has a
stationary point at (0, 0) and calculate the discriminant at this
point. b. Show that along any line through the origin, f(x, y) has
a local minimum at (0, 0)

Let f(x,y) = 3x^2 + cos(Pi*y). a) f has a saddle point at (0,k)
whenever k is an odd integer b) f has a saddle point at (0,k)
whenever k is an even integer) c) f has a local maximum at (0,k)
whenever k is an even integer d) f has a local minimum at (0,k)
whenever k is an odd integer.

Find the absolute minimum and absolute maximum of
f(x,y)=10−3x+8y
on the closed triangular region with vertices (0,0),(8,0) and
(8,12).
List the minimum/maximum values as well as the point(s) at which
they occur. If a min or max occurs at multiple points separate the
points with commas.

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).

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

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*

(3)If H(x, y) = x^2 y^4 + x^4 y^2 + 3x^2 y^2 + 1, show that H(x,
y) ≥ 0 for all (x, y). Hint: find the minimum value of H.
(4) Let f(x, y) = (y − x^2 ) (y − 2x^2 ). Show that the origin
is a critical point for f which is a saddle point, even though on
any line through the origin, f has a local minimum at (0, 0)

Find the area of one loop of the polar curve r=4*sin(3*theta +
Pi/3)
Let f(x,y) = 3x^2 + cos(Pi*y). a) f has a saddle point at (0,k)
whenever k is an odd integer b) f has a saddle point at (0,k)
whenever k is an even integer) c) f has a local maximum at (0,k)
whenever k is an even integer d) f has a local minimum at (0,k)
whenever k is an odd integer

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...

f (x, y) =(x ^ 4)-8(x ^ 2) + 3(y ^ 2) - 6y
Find the local maximum, local minimum and saddle points of the
function.
Calculate the values of the function at these points

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 24 minutes ago

asked 41 minutes ago

asked 43 minutes ago

asked 48 minutes ago

asked 53 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