A certain paper-cutting machine produces various sizes when increasing the length of a rectangular paper by 6 cm each second while simultaneously decreasing its width by 5 cm each second. At a certain instant, the paper is a square with side of length 30 cm. What is the rate of change of the area of the paper at that instant?

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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Solve the following problem using
partial derivatives.
A certain paper-cutting machine produces various
sizes when increasing the length of a rectangular
paper by 6 cm each second while simultaneously
decreasing its width by 5 cm each second. At a
certain instant, the paper is a square with side of
length 30 cm. What is the rate of change of the area
of the paper at that instant?

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