# Application in the derivative ..?

• Jan 27th 2010, 06:06 AM
explore
Application in the derivative ..?
I hope that someone help me in solving these application. (plz, I want to solution step by step)..

Q1:

A Cassna plane takes off from an airport at sea level and it's altitude (in feet) at time t (in minutes) is
given by h= 2000 ln (t+1) .
find the rate of climb at time t = 3min .

Q2:

If the variable sound power W is given by W = T^2 + t + 1 , Find the rate of change of the sound
pressure P , at time t= 3 s .

Q3:

A computer is programmed to inscribe a series of rectangle in the first quadrant under the curve of y=e^-x
What is the greatest area of the largest rectangle that can be inscribed ? .

Q4:

A point moves along the x axis so that it's position x at time t is specificed by the function x(t)= t^3-8t+8 .
determine the following :
a- the acceleration at times when the velocity is zero .
b- the average velocity over the time interval (0,6) .

I'm sorry for all this quastion ..
• Jan 27th 2010, 06:57 AM
Soroban
Hello, explore!

Quote:

Q3: A computer is programmed to inscribe a series of rectangles
in the first quadrant under the curve of $y\,=\,e^{-x}$

What is the greatest area of the largest rectangle that can be inscribed?

Code:

            |       *    |         *  |             *             |  *             + - - - - *             |:::::::::|y      *             |:::::::::|                *       - - - + - - - - * - - - - - - - - - -             |    x

The area of the rectangle is: . $xy$

So we have the area function: . $A \:=\:x\cdot e^{-x}$

Maximize it . . .

• Jan 27th 2010, 06:57 AM
artvandalay11
if you know that you need to use the derivative, then where are you having trouble with these?
• Jan 27th 2010, 11:33 AM
explore
Quote:

Originally Posted by Soroban
Hello, explore!

Code:

            |       *    |         *  |             *             |  *             + - - - - *             |:::::::::|y      *             |:::::::::|                *       - - - + - - - - * - - - - - - - - - -             |    x
The area of the rectangle is: . $xy$

So we have the area function: . $A \:=\:x\cdot e^{-x}$

Maximize it . . .

NICE ^_^ .. But what is the next step after we found the area function ??

Quote:

Originally Posted by artvandalay11
if you know that you need to use the derivative, then where are you having trouble with these?

I know that my friend ^_^ .. I can't solve these problem ^_^ because I don't know when, why and where I will use the derivative ??
• Jan 27th 2010, 11:34 AM
emathinstruction
for the second one, you need to find the rate of change (a.k.a. the value of the derivative) at t=3,... so take a derivative and plug in 3 for t

using the same idea you should be able to do 1