Answered: An accessories company finds that the…

An accessories company finds that the cost, in dollars, of producing x belts is given by C(x)=780+37x−0.062x^2. Find the rate at which average cost is changing when 178 belts have been produced

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter3: Linear And Nonlinear Functions

Section: Chapter Questions

Problem 26MCQ

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Question

100%

An accessories company finds that the cost, in dollars, of producing x belts is given by

C(x)=780+37x−0.062x^2.

Find the rate at which average cost is changing when

178

belts have been produced.

Expert Solution

Step 1

To find: The rate at which average cost is changing when 178 belts have been produced.

Given:

The cost function is $C (x) = 780 + 37 x - 0.062 x^{2}$

Concept used:

Average cost is $A = \frac{C (x)}{x}$

Power rule of differentiation: $\frac{d}{d x} (x^{n}) = n x^{n - 1}$

$Quotient Rule : {(\frac{f}{g})}^{'} = \frac{f' \cdot g - g' \cdot f}{g^{2}}$

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