Maximize
f(x)=4x-1.8x^(2) 1.2x^(3)-0.3x^(4)
a) Using Golden-Section Search (
x_(l)=-2,x_(u)=4,10 Iterations)
b) Using Newton's Method (
x_(0)=3,\epsi _(a)=1% )
Find the gradient vector and Hessian matrix for the given functions
a)
f(x,y)=ln(x^(2) 2xy 3y^(2))
Find and classify all the critical points for the given functions.
a)
f(x,y)=(y-2)x^(2)-y^(2)
b)
f(x,y)=7x-8y 2xy-x^(2) y^(3)
c)
f(x,y)=(3x 4x^(3))(y^(2) 2y)
For the given datasets find the followings.
a) Linear regression equation and its coefficient of determination (
r^(2) ).
\table[[
x,1,2,3,4,5,6,7],[
y,0.5,2.5,2,4,3.5,6,5.5]]
b) Polynomial regression equation and its coefficient of determination (
r^(2) ).
\table[[
x,0,1,2,3,4,5],[
y,2.1,7.7,13.6,27.2,40.9,61.1]]
c) Multiple linear regression equation and its coefficient of determination (
r^(2) ).
\table[[
x_(1),0,0,1,2,0,1],[
x_(2),0,2,2,4,4,6],[
y,14,21,11,12,23,23]]
