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. .
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. .
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 =
, 0 ≤ t ≤ 4
| 17t2 |
| 4 + t2 |
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 =
or at approximately ---Select--- 8:02 P.M. 8:18 P.M. 8:09 P.M. 7:45 P.M. 8:31 P.M. .2√3
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