Find the intervals of inc and dec & local max and min of h(x)=x^3/2-256x? using 1st derivative test.?

thanks...this one is really getting me!!!(Doh)

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- August 13th 2008, 09:50 PMmonolithintervals using 1st derivative test??
**Find the intervals of inc and dec & local max and min of h(x)=x^3/2-256x? using 1st derivative test.?**

thanks...this one is really getting me!!!(Doh) - August 13th 2008, 09:53 PMChris L T521
- August 13th 2008, 09:57 PMmonolithsorry
i guess i wasnt using proper scripting...it is the first one you have written

- August 13th 2008, 10:49 PMChris L T521
First find :

Now set this equal to zero:

This is the only critical point. So we investigate the behavior of over the intervals

Pick a point in these intervals and plug them into , for simplicity, I'll pick 1 and 360,000 (the last one seems large, but when we take the square root of it, we get a nice number to work with...no decimals involved).

It is decreasing here.

It is increasing here.

So to answer the first part of the question, the interval where its:

increasing --

decreasing --

where

Now, take note that a maximum occurs when a function goes from increasing to decreasing at a critical point, and a minimum occurs when a function goes from decreasing to increasing at a critical point. Which one do you think it is? What is the coordinates of the maximum/minimum? I leave that for you to do.

I hope this makes sense! (Sun)

--Chris