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Chapter 3: Q 39. (page 299)

Suppose the sides of a cube are expanding at a rate of 2inches per minute.

How fast is the volume of the cube changing at the moment that the cube has a side length of 8inches?

Short Answer

Expert verified

The rate of change in volume is384in3/min

Step by step solution

01

Step 1. Given Information

It is given that

dsdt=2in/min,s=8in

02

Step 2. Setting up the rate of change of the volume equation 

The formula for the volume of a cube is

V=s3

where

V is the volume of a cube

s is the side length

Find the derivative with respect to t

dVdt=3s2dsdt

03

Step 3. Finding the rate of change in Volume

Plug values dsdt=2in/min,s=8ininto volume derivative

dVdt=3s2dsdtdVdt=3(8)2脳2dVdt=384in3/in

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Most popular questions from this chapter

For each set of sign charts in Exercises 53鈥�62, sketch a possible graph of f.

Use the first derivative test to determine the local extrema of each function in Exercises 39- 50. Then verify your algebraic answers with graphs from a calculator or graphing utility.

f(x)=1+x+x2x2+x-2

Use a sign chart for f'to determine the intervals on which each function fis increasing or decreasing. Then verify your algebraic answers with graphs from a calculator or graphing utility.

f(x)=cos2(x)

For the graph of f in the given figure, approximate all the values x 鈭� (0, 4) for which the derivative of f is zero or does not exist. Indicate whether f has a local maximum, minimum, or neither at each of these critical points.

Use the definition of the derivative to find f' for each function f.

f(x)=x3+2
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