# Re: marginal cost

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Posted by Soroban on August 31, 2002 at 02:09:37:

In Reply to: Re: marginal cost posted by Sarah on August 30, 2002 at 21:04:47:

: Sorry. Please ignore the last question as there is a mistake in the equation.
: How does one proof that the marginal cost is a decreasing convex function of x?

: : MC= 20+5x^-1/2

Sarah,

I'm not familiar with "margin cost" problems, but
I think I know that a "decreasing convex function" is.

I only retired from teaching last fall, but I've
found that "concave" and "convex" is already in
use to describe what used to be "concave up" and
"concave down".

I'm still not sure which way "convex" goes - but
from the nature of this problem, I'll guess that
it's bowl-shaped, like a U.

M = 20 + 5x^(-1/2). Note that x > 0.

M' = -5/2x^(3/2)
For all x, M' is negative. Hence, M is always
decreasing.

M" = 15/4x^(5/2)
For all x, M" is positive. Hence, the graph of M
is always concave up. \__/

(I hope that's "convex"!)

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