The length, width, and height (denoted l, w andh respectively) of a rectangular box are changing over time. At the moment, we have l = 6 meters, w = 4 meters, and h = 2 meters. We also know the rate at which each side is changing: dl = Im / sec dt dw = lm / sec dt dh = -lm / sec dt (a) At the moment, is the volume of the box increasing, decreasing, or staying constant? If it is changing, at what rate is it changing? (Remember to include units in your answer.) (b) At the moment, is the surface area of the box increasing, decreasing, or staying constant? If it is changing, at what rate is it changing? (Remember to include units in your answer.)

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter4: Polynomial And Rational Functions
Section4.3: Zeros Of Polynomials
Problem 67E
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The length, width, and height (denoted l, w and h respectively) of a rectangular box are changing over time.
At the moment, we have l = 6 meters, w = 4 meters, and h=2 meters. We also know the rate at which each side is changing:
dl
= Im / sec
dt
dw
Im / sec
dt
dh
= -lm / sec
dt
(a) At the moment, is the volume of the box increasing, decreasing, or staying constant? If it is changing, at what rate is it changing? (Remember to include units in your answer.)
(b) At the moment, is the surface area of the box increasing, decreasing, or staying constant? If it is changing, at what rate is it changing? (Remember to include units in your answer.)
Transcribed Image Text:The length, width, and height (denoted l, w and h respectively) of a rectangular box are changing over time. At the moment, we have l = 6 meters, w = 4 meters, and h=2 meters. We also know the rate at which each side is changing: dl = Im / sec dt dw Im / sec dt dh = -lm / sec dt (a) At the moment, is the volume of the box increasing, decreasing, or staying constant? If it is changing, at what rate is it changing? (Remember to include units in your answer.) (b) At the moment, is the surface area of the box increasing, decreasing, or staying constant? If it is changing, at what rate is it changing? (Remember to include units in your answer.)
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