SOLUTION: THE COST IN MILLIONS OF DOLLARS FOR A COMPANY TO MANUFACTUREX THOUSAND AUTOMOBILES IS GIVEN BY THE FUNCTION C(X)=4X^2-16X+32. fIND THE NUMBER OF AUTOMOBILES THAT MUST BE PRODUCED T

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Question 1147314: THE COST IN MILLIONS OF DOLLARS FOR A COMPANY TO MANUFACTUREX THOUSAND AUTOMOBILES IS GIVEN BY THE FUNCTION C(X)=4X^2-16X+32. fIND THE NUMBER OF AUTOMOBILES THAT MUST BE PRODUCED TO MINIMIZE THE COST
Answer by ikleyn(52772)   (Show Source): You can put this solution on YOUR website!
.

For any quadratic function y = ax^2 + bx + c with positive value of the leading coefficient "a", it achieves the minimum at


    x = .


In your case,  a= 4, b= -16, so it achieves the minimum at  x=   =  = 2.


ANSWER.   2 thousand automobiles

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On finding the maximum/minimum of a quadratic function, see the lessons
    - HOW TO complete the square to find the minimum/maximum of a quadratic function
    - Briefly on finding the minimum/maximum of a quadratic function
    - HOW TO complete the square to find the vertex of a parabola
    - Briefly on finding the vertex of a parabola
in this site.

Also,  you have this free of charge online textbook in ALGEBRA-I in this site
    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.

The referred lessons are the part of this textbook under the topic "Finding minimum/maximum of quadratic functions".


Save the link to this online textbook together with its description

Free of charge online textbook in ALGEBRA-I
https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson

to your archive and use it when it is needed.


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