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The cost (in dollars) of producing x units of a certain commodity is C(x) = 5000 + 9x + 0.15x2. (a) Find the average rate of change of C with respect to x when the production level is changed from x = 100 to the given value. (Round your answers to the nearest cent.) (1) x = 102 per unit (ii) X = 101 per unit (b) Find the instantaneous rate of change of C with respect to x when x = 100. (This is called the marginal cost.) per unit

The cost (in dollars) of producing x units of a certain commodity is C(x) = 5000 + 9x + 0.15x2. (a) Find the average rate of change of C with respect to x when the production level is changed from x = 100 to the given value. (Round your answers to the nearest cent.) (1) x = 102 per unit (ii) X = 101 per unit (b) Find the instantaneous rate of change of C with respect to x when x = 100. (This is called the marginal cost.) per unit

Big Ideas Math A Bridge To Success Algebra 1: Student Edition 2015
Big Ideas Math A Bridge To Success Algebra 1: Student Edition 2015
1st Edition
ISBN:9781680331141
Author:HOUGHTON MIFFLIN HARCOURT
Publisher:HOUGHTON MIFFLIN HARCOURT
Chapter8: Graphing Quadratic Functions
Section: Chapter Questions
Problem 17CT
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The cost (in dollars) of producing x units of a certain commodity is C(x) = 5000 + 9x + 0.15x2. (a) Find the average rate of change of C with respect to x when the production level is changed from x = 100 to the given value. (Round your answers to the nearest cent.) (i) x = 102 $ per unit (ii) x = 101 %24 per unit (b) Find the instantaneous rate of change of C with respect to x when x = 100. (This is called the marginal cost.) $ per unit
Transcribed Image Text:The cost (in dollars) of producing x units of a certain commodity is C(x) = 5000 + 9x + 0.15x2. (a) Find the average rate of change of C with respect to x when the production level is changed from x = 100 to the given value. (Round your answers to the nearest cent.) (i) x = 102 $ per unit (ii) x = 101 %24 per unit (b) Find the instantaneous rate of change of C with respect to x when x = 100. (This is called the marginal cost.) $ per unit
Expert Solution
Step 1
  • Average Rate of change of C(x) with respect to x from x=a to x=b is C(b)-C(a)b-a.
  • Instantaneous Rate of change of C with respect to 'x' when x=a is C'(a) .
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