Question

Find the critical point of the function g(x)=ln(x^(2)+2x+3). Then determine whether the critical point is a local minimum or local maximum.

Answer #1

Find the linear approximation to g(x)=ln(x^2+2x+3) at the
critical point x=-1. Then using the same function, find the
quadratic approximation to g(x) at the critical point x=-1.

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).

(1 point) The function f(x)=−2x^3+21x^2−36x+11 has one local
minimum and one local maximum.
This function has a local minimum at x equals ______with value
_______and a local maximum at x equals_______ with value_______

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

f(x)=x^3-4x^2+5x-2
Find all critical numbers of the function, then use the second
derivative test on each critical number to determine if it is a
local maximum or minimum. Show your work.

a) The function f(x)=ax^2+8x+b, where a and b are
constants, has a local maximum at the point (2,15). Find the values
of a and b.
b) if b is a positive constand and x> 0, find the
critical points of the function g(x)= x-b ln x, and determine if
this critical point is a local maximum using the second derivative
test.

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

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=

1. At x = 1, the function g( x ) = 5x ln(x) −
3x
is . . .
Group of answer choices
has a critical point and is concave up
decreasing and concave up
decreasing and concave down
increasing and concave up
increasing and concave down
2. The maximum value of the function f ( x ) = 5xe^−2x
over the domain [ 0 , 2 ] is y = …
Group of answer choices
10/e
0
5/2e
e^2/5...

Find the maximum of the following function:
h(x, y) = ln(x^20 y^20)
given the constraints: 2x^2 + 2y^2 = 5,
x > 0, y > 0.

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