Consider the following function. g(x, y) = e− 4x^2 + 4y^2 + 8
√ 8y (a)...
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...
Consider the following function.
f (x, y) = (x −
6) ln(x5y)
(a)
Find the critical...
Consider the following function.
f (x, y) = (x −
6) ln(x5y)
(a)
Find the critical point of f.
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).
one of: relative max, relative...
Let f (x, y) = (x −
9) ln(xy).
(a)
Find the the critical point (a, ...
Let f (x, y) = (x −
9) ln(xy).
(a)
Find the the critical point (a, b). Enter the
values of a and b (in that order) into the answer
box below, separated with a comma.
(b)
Classify the critical point.
(A) Inconclusive (B) Relative Maximum (C) Relative Minimum (D)
Saddle Point
Examine the function f(x, y) = 2x 2 + 2xy + y 2 + 2x −...
Examine the function f(x, y) = 2x 2 + 2xy + y 2 + 2x − 3 for
relative extrema.
Use the Second Partials Test to determine whether there is a
relative maximum, relative minimum, a saddle point, or insufficient
information to determine the nature of the function f(x, y) at the
critical point (x0, y0), such that fxx(x0, y0) = −3, fyy(x0, y0) =
−8, fxy(x0, y0) = 2.
Let f(x,y) = e-x^2 + 5y^2 - y. Use the
Second Partials Test to determine which...
Let f(x,y) = e-x^2 + 5y^2 - y. Use the
Second Partials Test to determine which of the following is
true.
A) f(x,y) has a saddle point at (0, 1/10)
B) f(x,y) has a relative minimum at (0, 1/10)
C) f(x,y) has a relative maximum at (0, 10)
D) f(x,y) does not have a critical point at (0, 1/10)
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
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...
Find and classify each critical point (as relative maximum,
relative minimum, or saddle point) of
f(x,y)...
Find and classify each critical point (as relative maximum,
relative minimum, or saddle point) of
f(x,y) = 2x^3 + 3x^2 + y^1 - 36x + 8y + 1
question #1: Consider the following function.
f(x) =
16 − x2,
x ≤ 0
−7x,
x...
question #1: Consider the following function.
f(x) =
16 − x2,
x ≤ 0
−7x,
x > 0
(a) Find the critical numbers of f. (Enter your answers
as a comma-separated list.)
x =
(b) Find the open intervals on which the function is increasing or
decreasing. (Enter your answers using interval notation. If an
answer does not exist, enter DNE.)
increasing
decreasing
question#2:
Consider the following function.
f(x) =
2x + 1,
x ≤ −1
x2 − 2,
x...