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? STEP 1: STEP 2: STEP 3: STEP 4: STEP 5: STEP 6: STEP 7: N = 12t² 4+2 Begin by finding the first derivative of N. 961(2-4)-2 N'(t) 961 = 0sts 4 Find the second derivative of N. N"(t) = Solve for t by setting the second derivative of N equal to zero. Find the third derivative of N. N"(t) = 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"" = State the sign of N"""(t). N'"(t)?0 Select the most appropriate response. The student is assembling components at the greatest rate when t or at approximately ---Select---.
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? STEP 1: STEP 2: STEP 3: STEP 4: STEP 5: STEP 6: STEP 7: N = 12t² 4+2 Begin by finding the first derivative of N. 961(2-4)-2 N'(t) 961 = 0sts 4 Find the second derivative of N. N"(t) = Solve for t by setting the second derivative of N equal to zero. Find the third derivative of N. N"(t) = 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"" = State the sign of N"""(t). N'"(t)?0 Select the most appropriate response. The student is assembling components at the greatest rate when t or at approximately ---Select---.
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 the function below. At what
time is the student assembling components at the greatest rate?
STEP 1:
STEP 2:
STEP 3:
STEP 4:
STEP 5:
STEP 6:
STEP 7:
12t²
4 + 12'
Begin by finding the first derivative of N.
N =
N'(t) = 96t (t²-4)-2
Find the second derivative of N.
N"(t) =
0 ≤t≤ 4
Solve for t by setting the second derivative of N equal to zero.
t =
Find the third derivative of N.
N"(t) =
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" =
State the sign of N""(t).
N"(t) ? 0
Select the most appropriate response.
The student is assembling components at the greatest rate when t =
or at approximately ---Select--- ✓
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