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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 the student assembling components at the greatest rate?

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 the student assembling components at the greatest rate?

College Algebra
College Algebra
1st Edition
ISBN:9781938168383
Author:Jay Abramson
Publisher:Jay Abramson
Chapter3: Functions
Section3.3: Rates Of Change And Behavior Of Graphs
Problem 46SE: Near the surface of the moon, the distance that an object falls is a function of time. It is given...
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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? 19t? N = 0 <t< 4 4 + t2' STEP 1: Begin by finding the first derivative of N. 152t (4 + ?)² N'(t) STEP 2: Find the second derivative of N. 628 – 4562 (4+ ?)3 N"(t) STEP 3: Solve for t by setting the second derivative of N equal to zero. 2 t = V3' V3 STEP 4: Find the third derivative of N. 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"' %D V ---Select--- STEP 6: State the sign of N"''(t). 8:31 P.M. N''(t) > v 0 8:09 P.M. 7:45 P.M. STEP 7: Select the most appropriate response. 8:18 P.M. 8:02 P.M. The student is assembling components at the greatest rate when t = or at approximately -Select--- v
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? 19t? N = 0 <t< 4 4 + t2' STEP 1: Begin by finding the first derivative of N. 152t (4 + ?)² N'(t) STEP 2: Find the second derivative of N. 628 – 4562 (4+ ?)3 N"(t) STEP 3: Solve for t by setting the second derivative of N equal to zero. 2 t = V3' V3 STEP 4: Find the third derivative of N. 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"' %D V ---Select--- STEP 6: State the sign of N"''(t). 8:31 P.M. N''(t) > v 0 8:09 P.M. 7:45 P.M. STEP 7: Select the most appropriate response. 8:18 P.M. 8:02 P.M. The student is assembling components at the greatest rate when t = or at approximately -Select--- v
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