Let f(x, y) = 2x^3 − 6xy + 3y^2 be a function defined on
xy-plane
(a) Find first and second partial derivatives of.
(b) Determine the local extreme points of f (max., min., saddle
points) if there are any.
(c) Find the absolute max. and absolute min. values of f over
the closed region bounded by the lines x = 2, y = 0, and y = x
let f(x)=(x^2 + 2x) / (x - 1)^2
a) Find the domain and if any intercepts
b)find the horizontal asymptotes
c) find the vertical asymptotes
d)find the intervals on which the function is increasing and
decreasing and identify the function's local extreme values,
critical values
e)identify the concavity and if any the point of inflection
f) graph the function
Consider the function f(x, y) = 3+xy−x−2y. Let D be the closed
triangular region with vertices (1, 4), (5, 0), and (1, 0). Find
the absolute maximum and the absolute minimum of f on D.
Let
f(x) = 14 −
2x.
(a)
Sketch the region R under the graph of f on
the interval
[0, 7].
The x y-coordinate plane is given. There is 1
line and a shaded region on the graph.
The line enters the window at y = 13 on the positive
y-axis, goes down and right, and exits the window at
x = 6.5 on the positive x-axis.
The region is below the line.
The x y-coordinate plane is given. There...
Given two planes 2x - y + z = 7 and x + 3y - 4z = 1.
(a) Give an orthogonal vector to each plane.
(b) Do the planes intersect? Why or why not?
(c) If they intersect, find the parametric equation of the
intersection line, if not, find the distance of both planes.
5. Consider the function f(x) = -x^3 + 2x^2 + 2.
(a) Find the domain of the function and all its x and y
intercepts.
(b) Is the function even or odd or neither?
(c) Find the critical points, all local extreme values of f, and
the intervals on which f is increasing or decreasing.
(d) Find the intervals where f is concave up or concave down and
all inflection points.
(e) Use the information you have found to sketch...