How do you find the number of units x that produce a minimum cost C if C=0.01x^2-90x+15000.?

How do you also find on the calculator? Thanks.

How do you find the number of units x that produce a minimum cost C if C=0.01x^2-90x+15000.?
OK





C = .01x^2 -90x +15000





Take first derivitive, and where this = 0 is max/min point





0=.02x -90


90 = .02x





4500 = x





At x = 4500





C = .01(4500)^2 - 90(4500) + 15000


C = 202,500 - 405,000 + 15,000


C = -187,500





Hope that helps.
Reply:This is a concave curve opening upward, this to find the minimum, we need to know when the derivative = 0 (that is, when a line tangent to the curve is parallel to the x-axis, which would represent the minimum value of the curve).





C' = 0.02x - 90


0.02x - 90 = 0


0.02x = 90


x = 90/0.02


x = 4500 units





Hope this helps! :)
Reply:well, considering that this equation is parabolic,......


the parabola opens up, and the vertical translation is up 15000 and it opens up from there, so the minimum cost of C must be the minimum value, which is 15000.


on the calculator, you would set x equal to 0 which still ends up being 15000
Reply:on a calculator, sketch the curve and trace along the graph till you reach the minimum point.





to do this analytically, take the derivative and set it equal to zero.

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