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 th what time is the student assembling components at the greatest rate? 13t? N = 0 sts 4 4 + t2' STEP 1: Begin by finding the first derivative of N. 104t N'(t) = (4 + P)? STEP 2: Find the second derivative of N. 104(4 – 32) (?+4)3 N"(t) = STEP 3: Solve for t by setting the second derivative of N equal to zero. 2 STEP 4: Find the third derivative of N. 624(? – 4) (P+4)4 N"(t) = 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"" = 4.02 STEP 6: State the sign of N'(t). N'(t)
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 th what time is the student assembling components at the greatest rate? 13t? N = 0 sts 4 4 + t2' STEP 1: Begin by finding the first derivative of N. 104t N'(t) = (4 + P)? STEP 2: Find the second derivative of N. 104(4 – 32) (?+4)3 N"(t) = STEP 3: Solve for t by setting the second derivative of N equal to zero. 2 STEP 4: Find the third derivative of N. 624(? – 4) (P+4)4 N"(t) = 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"" = 4.02 STEP 6: State the sign of N'(t). N'(t)
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Transcribed Image Text: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 th
what time is the student assembling components at the greatest rate?
13t2
N =
4 + t2'
0sts4
STEP 1:
Begin by finding the first derivative of N.
104t
N'(t) =
(4 + ?)?
STEP 2:
Find the second derivative of N.
104(4 – 3?)
(P + 4)3
N"(t) =
STEP 3:
Solve for t by setting the second derivative of N equal to zero.
2
t =
V3
STEP 4:
Find the third derivative of N.
6241(? – 4)
(?+ 4)4
N"'(t) =
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'" = 4.02
STEP 6:
State the sign of N''(t).
N'"'(t) <v
STEP 7:
Select the most appropriate response.
The student is assembling components at the greatest rate when t =
V3
or at approximately 8:09 P.M.
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