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- Apr 22nd 2011, 09:21 PM #1

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## D(t) = (4t)/ (0.01t^2 +5.1)

For these I'm clueless. Please help

5) Function D(t) = (4t)/(0.01t^2+5.1). Given the concentration, D, of a drug in bloodstream where D is measured in micrograms per milliliter and t is minutes from the time the drug is taken. What's the maximum concentration of the drug found in bloodstream at any time?

A) 0.01 micrograms/ milliliters

B) 4 micrograms/ milliliters

C) 5.1 micrograms/ milliliters

D) 8.856 micrograms/ milliliters

E) 22.583 micrograms/ milliliters

- Apr 22nd 2011, 09:35 PM #2

- Apr 22nd 2011, 09:38 PM #3

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- Apr 22nd 2011, 09:49 PM #4
AM-GM inequality states that if a>0 and b>0 then a+b >= 2(sqrt(ab))

you could also check this out Inequality of arithmetic and geometric means - Wikipedia, the free encyclopedia

- Apr 23rd 2011, 09:58 AM #5

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"AM-GM": Arithmetic Mean- Geometric Mean. The arithmetic mean of two numbers is (a+ b)/2. The geometric mean of two numbers is \sqrt{ab}. The "Arithmetic Mean-Geometric Mean inequality" says that the arithmetic mean is always less than equal to the geometric mean.

(More geherally, the arithmetic mean of n numbers, a_1, a_2, \cdot\cdot\cdot, a_n is \frac{a_1+ a_2+ \cdot\cdot\cdot+ a_n}{n} and the geometric mean is \sqrt[n]{a_1a_2\cdot\cdot\cdot a_n}. There is also the "harmonic mean". The harmonic mean of 2 numbers is \frac{2}{\frac{1}{a}+ \frac{1}{b}}. The harmonic mean of n numbers is \frac{n}{\frac{1}{a_1}+ \frac{1}{a_2}+ \cdot\cdot\cdot+ \fra{1}{a_n}}

- Apr 23rd 2011, 09:07 PM #6

- Apr 24th 2011, 06:32 AM #7

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- Apr 24th 2011, 06:08 PM #8