21.T. Let f be defined on D = {(§, n) e R:{ > 0, 1 > 0} to R by the formula %3D f(E, n) 1 1 +:+ cEn. Locate the critical points of f and determine whether they yield relative maxima, relative minima, or saddle points. If c > 0 and we set Di = { (}, n):; > 0, n > 0, § + 1 < c}, then locate the relative extrema of ƒ on Dj. 21.U. Suppose we are given n points (§j, n;) in R² and desire to find the linear function F(x) = Ax + B for which the quantity E F(;) – nd² is minimized. Show that this leads to the equations AE+BE t; = E im, j=1 AEi+ nB j=1 for the numbers A, B. This linear function is referred to as the linear function
21.T. Let f be defined on D = {(§, n) e R:{ > 0, 1 > 0} to R by the formula %3D f(E, n) 1 1 +:+ cEn. Locate the critical points of f and determine whether they yield relative maxima, relative minima, or saddle points. If c > 0 and we set Di = { (}, n):; > 0, n > 0, § + 1 < c}, then locate the relative extrema of ƒ on Dj. 21.U. Suppose we are given n points (§j, n;) in R² and desire to find the linear function F(x) = Ax + B for which the quantity E F(;) – nd² is minimized. Show that this leads to the equations AE+BE t; = E im, j=1 AEi+ nB j=1 for the numbers A, B. This linear function is referred to as the linear function
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:21.T. Let f be defined on D = {(*, n) E R²:¿ > 0, n > 0} to R by the formula
1
1
+
f(E, n) =
+ cEn.
Locate the critical points of f and determine whether they yield relative maxima,
relative minima, or saddle points. If c > 0 and we set
DI = {(}, n):{ > 0, n > 0, § + 1 < c},
then locate the relative extrema of f on D1.
21.U. Suppose we are given n points (, n;) in R? and desire to find the linear
function F(x) = Ax + B for which the quantity
E [F (;) – nil²
j=1
is minimized. Show that this leads to the equations
A E+BE ; = E im,
ΑΣ ξ
AE i; + nB
for the numbers A, B. This linear function is referred to as the linear function
which best fits the given n points in the sense of least squares.
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