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!!!
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!
--Chris