Suppose That $z = x ^ { 3 } y ^ { 2 }$

question 191

Essay

Suppose that $z = x ^ { 3 } y ^ { 2 }$ , where both $x$ and $y$ are changing with time. At a certain instant when $x = 1$ and $y = 2$ , $x$ is decreasing at the rate of 2 units/s and $y$ is increasing at the rate of 3 units/s. How fast is $Z$ changing at this instant? Is $Z$ increasing or decreasing?

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Definitions:

Partnership

A legal form of business operation where two or more individuals share ownership, as well as the responsibility for managing the business and the sharing of its profits and losses.

Personal Income Tax

A tax levied on an individual's income, including wages, salaries, and other earnings, by the government.

Benefits-Received Principle

A theory in tax policy stating that taxes should be levied in accordance with the level of government services and benefits an individual or entity receives.

Revenue

The income generated from normal business operations and includes discounts and deductions for returned merchandise.