Question

Consider the function given by f(x,y) = 3x2 −6xy + 2y3 +
23.

(a) Find all critical points of f(x,y) and determine their
nature.

(b) What are the minimum and maximum values of f(x,y) on the
straight line segment given by 0 ≤ x ≤ 3, y = 2?

Answer #1

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

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.

Consider the function f(x) = x3 − 2x2 − 4x + 9 on the interval
[−1, 3].
Find f '(x). f '(x) = 3x2−4x−4
Find the critical values. x =
Evaluate the function at critical values. (x, y) =
(smaller x-value)
(x, y) =
(larger x-value)
Evaluate the function at the endpoints of the given
interval.
(x, y) =
(smaller x-value)
(x, y) =
(larger x-value)
Find the absolute maxima and minima for f(x) on the interval
[−1, 3].
absolute...

2) A varying force F(x,y) = (3x2 – 6xy + 2) i is
applied to an object from (x=2 y=2) to (x=4 y=2). Force is in
Newtons and distances are measured in meters. Find the work
done.

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 intervals where the function f (x) = ln(x) + 3x2 − x is
concave up or concave down. Include a sign chart indicated critical
points and test values.

(9)
(a)Find the double integral of the function f (x, y) = x + 2y
over the region in the plane bounded by the lines x = 0, y = x, and
y = 3 − 2x.
(b)Find the maximum and minimum values of 2x − 6y + 5 subject to
the constraint x^2 + 3(y^2) = 1.
(c)Consider the function f(x,y) = x^2 + xy. Find the directional
derivative of f at the point (−1, 3) in the direction...

consider the function f(x) = x/1-x^2
(a) Find the open intervals on which f is increasing or
decreasing. Determine any local minimum and maximum values of the
function. Hint: f'(x) = x^2+1/(x^2-1)^2.
(b) Find the open intervals on which the graph of f is concave
upward or concave downward. Determine any inflection points. Hint
f''(x) = -(2x(x^2+3))/(x^2-1)^3.

Consider the equation below.
f(x) =
2x3 + 3x2
− 72x
(a) Find the interval on which f is increasing. (Enter
your answer in interval notation.)
Find the interval on which f is decreasing. (Enter your
answer in interval notation.)
(b) Find the local minimum and maximum values of f.
local minimum
local maximum
(c) Find the inflection point.
(x, y) =
Find the interval on which f is concave up. (Enter your
answer in interval notation.)
Find the...

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).

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