I need help solving 14.1.2 a,b,c, and d 274FUNCTIONS OF SEVERAL VARIABLES14.1.2 In each of the following cases, find the gradient vector and the Hessian matrix ofthe function f (x,y), and evaluate them at (1, –2).(b) f(x,y) = 3x²y³ + 2x°y?(c) f(x, y) = (3x – 2y)/(x² + y²) (d) f(x,y) = x ln(1+ y²)(a) f(x,y) = 3x? + 2y514.1.3 A monopolist sells quantities x and y respectively of products X and Y. The pricesPy charged for X and Y are given by the following functions:Px andPx = 25 – 2x + y,PY = 20 + x – y.noFind the total revenue and the marginal revenues of X and Y.The expressions formand functions; they generalise the inverse demand functions of Section 7and are discussed further in Chapter 16. Why would this question have beharder if you had been given the demand functions in direct rather than inve-form?Pxand pyin terms of quantities sold are called inverse de1.4 Two goods 1 and 2 have demand functions1/2-1/2x2 = 4p;' P2-2 1/2¤1 = 8p, P2where x; and P; denote respectively the quantity demanded and the prgood i. Find the own-price elasticity of demand for each good and the twotigitior of demand.

Since you have posted a question with multiple sub-parts, we will solve first three sub-parts for…

Answered: a) f(x,y) = 3x² + 2y5 (b) f(x,y) = 3a*y…

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a) f(x,y) = 3x² + 2y5 (b) f(x,y) = 3a*y %3D a) f(m a) - (3r - ?u)((T2 + y?) (d) f(x, y) = x ln(1+ y²) %3D

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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Concept explainers

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.

Question

I need help solving 14.1.2 a,b,c, and d

274
FUNCTIONS OF SEVERAL VARIABLES
14.1.2 In each of the following cases, find the gradient vector and the Hessian matrix of
the function f (x,y), and evaluate them at (1, –2).
(b) f(x,y) = 3x²y³ + 2x°y?
(c) f(x, y) = (3x – 2y)/(x² + y²) (d) f(x,y) = x ln(1+ y²)
(a) f(x,y) = 3x? + 2y5
14.1.3 A monopolist sells quantities x and y respectively of products X and Y. The prices
Py charged for X and Y are given by the following functions:
Px and
Px = 25 – 2x + y,
PY = 20 + x – y.
no
Find the total revenue and the marginal revenues of X and Y.
The expressions for
mand functions; they generalise the inverse demand functions of Section 7
and are discussed further in Chapter 16. Why would this question have be
harder if you had been given the demand functions in direct rather than inve-
form?
Px
and py
in terms of quantities sold are called inverse de
1.4 Two goods 1 and 2 have demand functions
1/2-1/2
x2 = 4p;' P2
-2 1/2
¤1 = 8p, P2
where x; and P; denote respectively the quantity demanded and the pr
good i. Find the own-price elasticity of demand for each good and the two
tigitior of demand.

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