Analyze and sketch the curve y = x3 − 6x2 +
9x. A full analysis includes the following:
critical points, intervals of increase/decrease,
concavity, points of inflection, domain and range, intercepts.
Organize your work in chart form.
For this problem, consider the function f(x) = x3 - 9x2 +15x + 3.
A. Determine the intervals on which f(x) is increasing and intervals on which f(x) is decreasing.
B. Determine all relative (local) extrema of f(x).
C. Determine intervals on which f(x) is concave up and intervals on which f(x) is concave down.
D. Determine all inflection points of f(x).
Consider the linear system of equations
2x1 − 6x2 − x3 = −38
−3x1 − x2 + 7x3 = −34
−8x1 + x2 − 2x3 = −20
With an initial guess x (0) = [0, 0, 0]T solve the system using
Gauss-Seidel method.
ƒ(x,y)= x3 + 3xy2 - 15x + y3 -
15y
For this question i need to calculate the critical points and
all local minima, local maxima and saddle points. How should this
be done?
Consider the following linear optimization model.
Z = 3x1+ 6x2+ 2x3
st 3x1 +4x2 + x3 ≤2
x1+
3x2+ 2x3 ≤ 1
X1, x2, x3 ≥0
(10) Write the optimization problem in standard form with the
consideration of slack variables.
(30) Solve the problem using simplex tableau method.
(10) State the optimal solution for all variables.
Find the coordinates of all local extrema and inflections of y =
x − 4√x. Give the intervals where the function is increasing,
decreasing, concave up, and concave down.
1. Solve the following system:
2x1- 6x2- x3 = -38
-3x1–x2 +7x3 = -34
-8x1 +x2 – 2x3 = -20
By:
a. LU Factorization
b. Gauss-Siedel Method, error less that10-4
Hint (pivoting is needed, switch rows).
For the function f(x,y) = 4xy - x^3 - 2y^2 find and label any
relative extrema or saddle points. Use the D test to classify. Give
your answers in (x,y,z) form. Use factions, not decimals.
5. Explain (concisely) along with a labelled diagram the
following terms: a) local or relative extrema b) absolute extrema
c) turning points d) inflection point e) critical points
Consider the following linear programming problem:
Z=$15X+$20Y
Subject to:
8X+5Y<=40
0.4X+Y>=4
Solve the values of x and y that will maximize revenue by using the
corner point method graphical approach to linear programming. What
revenue will result? Please show work.