Answered: A function f is called homogeneous of…

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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A function f is called homogeneous of degree n if it satisfies the equation

f(tx, ty) = tⁿf(x, y)

for all t, where n is a positive integer and f has continuous second-order partial derivatives. If f is homogeneous of degree n, show that

f_x(tx, ty) = t^{n − 1}f_x(x, y). (Hint: Use Chain Rule)

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on step 2) going from the first to the second arrow: where does the t come from on the right-hand side of the second arrow and why does the + partial/partial(ty) * f(tx,ty) *partial(ty)/partial(x) on the same side in the first arrow become 0 on the second arrow?

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