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. 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...
-- Find the linear approximation of the function f(x,y)= e^(x^2 + 4xy - 2y^2) at (1,2) using the aproximate f(0.99,2.01)
-- find Zvu for z= f(x,y), x=uv , y= v^2 + u^2
-
Using Matlab, consider the function f(x) =
x^3 – 2x + 4 on the interval [-2, 2] with h
= 0.25. Write the MATLAB function file to find the
first derivatives in the entire interval by all three methods i.e.,
forward, backward, and centered finite difference
approximations.
Could you please add the copiable Matlab code and the associated
screenshots? Thank you!
The Vector Field f(x, y) = (2x + 2y^2)i + (4xy - 6y^2)j has
exactly one potential function f (x, y) that satisfies f(0, 0).
Find this potential function , then find the value of this
potential function at the point (1, 1).
4. The joint density function of (X, Y ) is
f(x,y)=2(x+y), 0≤y≤x≤1
. Find the correlation coefficient ρX,Y
.
5. The height of female students in KU follows a normal
distribution with mean 165.3 cm and s.d. 7.3cm. The height of male
students in KU follows a normal distribution with mean 175.2 cm and
s.d. 9.2cm. What is the probability that a random female student is
taller than a male student in KU?
For the function f(x) = x^2 +3x / 2x^2 + 6x +3 find the
following, and use it to graph the function.
Find: a)(2pts) Domain
b)(2pts) Intercepts
c)(2pts) Symmetry
d) (2pts) Asymptotes
e)(4pts) Intervals of Increase or decrease
f) (2pts) Local maximum and local minimum values
g)(4pts) Concavity and Points of inflection and
h)(2pts) Sketch the curve
For the function f(x) = x^2 +3x / 2x^2 + 7x +3 find the
following, and use it to graph the function.
Find: a)(2pts) Domain
b)(2pts) Intercepts
c)(2pts) Symmetry
d) (2pts) Asymptotes
e)(4pts) Intervals of Increase or decrease
f) (2pts) Local maximum and local minimum values
g)(4pts) Concavity and Points of inflection and
h)(2pts) Sketch the curve
Consider the following function:
f (x , y , z ) = x 2 + y 2 + z 2 − x y − y z + x + z
(a) This function has one critical point. Find it.
(b) Compute the Hessian of f , and use it to determine whether
the critical point is a local man, local min, or neither?
(c) Is the critical point a global max, global min, or neither?
Justify your answer.