which of the following is a strength of a coroporation relative to
the other forms of business
a.
lower taxes
b. level of liability
c.low organization costs
d. level of government regulation
For the following exercises, use the table of values that represent points on the graph of a quadratic function. By determining the vertex and axis of symmetry, find the general form of the equation of the quadratic function.
Find the relative maximum and minimum values.
a. f(x,y)=x^3-6xy+y^2+6x+3y-1/5
Relative minimum: ________ at ________
Relative maximum: ________ at ________
b. f(x,y)= 3x-6y-x^2-y^2
Relative minimum: ________ at ________
Relative maximum: ________ at ________
1. a. Find the relative maximum and minimum values of f(x, y) =
(3x^2) − (2y^2) b. Find the relative maximum and minimum values of
f(x, y) = (x^3) + (y^3) − 6xy . The expression that you may need D
= fxx(x0,
y0)fyy(x0, y0) −
(fxy(x0, y0))2
For the following functions f and g
: f(x, y) = e ax − (1 − a)lny a > 0 g(x, y, z) = −3x 2 − 3y 2
− 3z 2 + 2xy + 2xz + 2yz
1.
Calculate the Hessian matrices of f and g noted Hf (x, y) and
Hg(x, y, z)
2. Show that Hg(x, y, z) is define negativly for all (x, y, z) ∈
Dg
3. For what value o a is , Hf...
1. What is a critical number of a function f ? What is the connection between critical numbers and relative extreme values?
2. What are inflection points? How do you find them?
Consider the following quadratic forms
q(x1, x2) = 3x1^2 − 6x1x2 + 11x2^2 and
r(x1, x2, x3) = x1^2 − x2^2+x3^2+ 2x1x2 − 6x1x3+2x2x3,
on R 2 and R 3 , respectively. In both cases do the
following.
(a) Find the symmetric matrix A representing the quadratic
form.
(b) Find a corresponding orthogonal matrix P of eigenvectors of
that matrix.
(c) Write down the maximum and minimum values of the quadratic
form over the unit vectors (in R 2 and...