Rolle's Theorem Word Problem?

Question

The ordering and transportation cost C of components used in manufacturing process is approximated by

C(x)= 10 (1/x + x/(x+3) )
where C is measured in thousands of dollars and x is the order size in hundreds

A.) Verfiy that C(3)=C(6)
B.) According to Rolle's Theorem, the rate of change of cost must be 0 for some order size in the interval [3/6] Find this order size in hundreds

It's for my AP Calc class, of course steps would be FANSTASTIC so I could figure out how to do this on my own but I'd more than happy with a step or two. Thanks

Answer 1

"is approximated by C(x)= 10 (1/x + x/(x+3) )"

It would be good to have some idea how this function looks like. Easy way how to do it is by using on-line program http://rechneronline.de/function-graphs/. It may take some time till you will be familiar with all its possibilities (perhaps some half an hour). But it is a useful tool for drawing functions, their derivatives and antiderivatives, calculating values etc.

"A.) Verify that C(3)=C(6)"

Have you did it? What was the result? [I hope that 8.333]

"B.) According to Rolle's Theorem,"

I suppose you know this theorem.

"the rate of change of cost must be 0 for some order size in the interval [3/6] Find this order size in hundreds"

Rate of change is derivative. Now find the derivative of the function C(x) and find such value of x for which this derivative is equal zero. Ready? If the result is $ 4100, then accept my congratulation.

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