Problem

Solve the given problems by finding the appropria…

Problem 36 Easy Difficulty

Solve the given problems by finding the appropriate derivative.
In a study of traffic control, the number $n$ of vehicles on a certain section of a highway from 2 p.m. to 8 p.m. was found to be $n=200\left(1+t^{3} e^{-t}\right),$ where $t$ is the number of hours after $2 \mathrm{p} . \mathrm{m}$ At what time is the number of vehicles the greatest?

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Calculus 1 / AB

Basic Technical Mathematics with Calculus

Chapter 27

Differentiation of Transcendental Functions

Section 8

Applications

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Video Transcript

we need to find the time in which the number and of vehicles in the sermon section of the home From 12 p.m. From two pm to eight pm. This and its greatest. So the number of vehicles is given by the function end mm hmm. 200 tom one plus T Plus 2/3 times sweeter than negativity. Where she is the total number of hours after two PM. To find the greatest value of our functions. First we have to calculate its the revenue And he created 20 to find the critical points. So the first derivative of this function, the N. D. T. It's equal to using integration by parts to a value in this, the living is okay. 200 time Deep to the 3rd times negative game to the negative chief plus three. The square times E to the negative team. Then we just sent this derivatives to be equal to zero. And because he said the -2 is always positive The values but he given between Germany and three. Therefore the M. This becomes E. To the negative T times two squared Times negative teeth, but three Is equal to zero. So the second derivative When N is equal to three, they will be equal to negative 89 point. See one

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Allyn J. Washington, Richard S. Evans

Basic Technical Mathematics with Calculus

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