Answered: Consider a college student who works…

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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Question

Consider a college student who works from 7 P.M. to 11 P.M. assembling mechanical components. The number N of components assembled after t hours is given by the function below. At what time is the student assembling components at the greatest rate?

N =

17t²

4 + t²

, 0 ≤ t ≤ 4

STEP 1:

Begin by finding the first derivative of N.

N'(t) =

136t(t2+4)2

STEP 2:

Find the second derivative of N.

N''(t) =

−136(3t2−4)(t2+4)3

STEP 3:

Solve for t by setting the second derivative of N equal to zero.

t =

2√3

STEP 4:

Find the third derivative of N.

N'''(t) =

1632t(t+2)(t−2)(t2+4)4

STEP 5:

Substitute the value for t from Step (3) into the equation for the third derivative of N. (Round your answer to two decimal places.)

N''' =

STEP 6:

State the sign of

N'''(t).

N'''(t) ? < > 0

STEP 7:

Select the most appropriate response.

The student is assembling components at the greatest rate when

t =

2√3

or at approximately ---Select--- 8:02 P.M. 8:18 P.M. 8:09 P.M. 7:45 P.M. 8:31 P.M. .

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