Use the derivitive to identify the open intervals on which the function is increasing or decreasing.
f(x)=x^3/4 - 3x

Question

Use the derivitive to identify the open intervals on which the function is increasing or decreasing. 
f(x)=x^3/4 - 3x

australopithecus · Answer

first off take the derivative

cinniomon · Answer

Ok

cinniomon · Answer

Then what

australopithecus · Answer

Then check to see where the derivative is 0, and then check the derivatives domain

australopithecus · Answer

to get the critical numbers

australopithecus · Answer

If you get a critical number that isn't in the domain of the original function do not use it

australopithecus · Answer

Give me the critical numbers you get

it is always smart to write on a test

set f'(x) = 0

australopithecus · Answer

that is worth a mark or part of a mark at least because it shows you know what you are doing

australopithecus · Answer

Once you give me the critical numbers I will show you how to figure out in what intervals your function is increasing and decreasing

cinniomon · Answer

Ok is one of the numbers the sq root of 8/3?

australopithecus · Answer

ok you only got one critical number?

australopithecus · Answer

I'm studying for an exam while helping you so you will have to do most of the work if that is alright

australopithecus · Answer

I can show you the method of solving it though

cinniomon · Answer

That would be great if you could show me the method and its fine if you r studying

australopithecus · Answer

just say you only have one critical number

Make a table like so:

|dw:1352772038576:dw|

Now plug in any number in the interal

$$(-\infty, \sqrt{\frac{8}{3}})$$

into f(x) and see if you get a positive or negative, the number doesn't matter just the sign

Do the same with this interval

$$(\sqrt{\frac{8}{3}},\infty)$$

Tell me what your results are and I will show you how to fill out the table