a.) What is the average cost C(x) per vest if x vests are produced in one​ day?   b.) Find the critical numbers of C(x)​, the intervals on which the average cost per vest is​ decreasing, the intervals on which the average cost per vest is​ increasing, and the local extrema.

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
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Chapter8: Polynomials
Section8.1: Adding And Subtracting Polynomials
Problem 58PPS
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A manufacturer incurs the following costs in producing x water ski vests in one​ day, for 0<x<150​: fixed​ costs, ​$500​; unit production​ cost, ​$25 per​ vest; equipment maintenance and​ repairs, 0.05x2 dollars.​ So, the cost of manufacturing x vests in one given day is given by C(x)=0.05x2+25x+500​,
where 0<x<150.
 
a.) What is the average cost C(x) per vest if x vests are produced in one​ day?
 
b.) Find the critical numbers of C(x)​, the intervals on which the average cost per vest is​ decreasing, the intervals on which the average cost per vest is​ increasing, and the local extrema.
 
 
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