.
C(x) = 0.2*x^2 - 1.3x + 10.35,
and they want you find x which minimizes this function.
For any quadratic function f(x) = ax^2 + bx + c with the positive coefficient "a", it gets the minimum at x = .
In your case a= 0.2, b= -1.3, so = = 6.5.
Since in this problem only integer values of x are meaningful, the problem has two solutions x= 6 or x= 7.
Both answers are equally good.
Solved.
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On finding 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.