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 whattime is the student assembling components at the greatest rate?STEP 1:STEP 2:STEP 3:STEP 4:STEP 5:STEP 6:STEP 7:12t²4 + 12'Begin by finding the first derivative of N.N =N'(t) = 96t (t²-4)-2Find the second derivative of N.N"(t) =0 ≤t≤ 4Solve 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) ? 0Select the most appropriate response.The student is assembling components at the greatest rate when t =or at approximately ---Select--- ✓

Answered: Image /qna-images/answer/ad789bfb-9a06-44e4-a5a1-2cb4eb165bde.jpg

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---.

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)

6th Edition

ISBN:9781337111348

Author:Bruce Crauder, Benny Evans, Alan Noell

Publisher:Bruce Crauder, Benny Evans, Alan Noell

Chapter5: A Survey Of Other Common Functions

Section5.3: Modeling Data With Power Functions

Problem 3TU

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