Could someone help me with functions and critical numbers?

Question

anonymous · Answer

Whats the questions

anonymous · Answer

I didn't quite understand how to figure out the sign of the derivative (whether it's greater or less than zero) depending on what interval you're looking at

anonymous · Answer

Is their a question to answer?

anonymous · Answer

A sample question is
$$f(x) = \frac{ 1 }{ 4 }x ^{4}-2x ^{2}$$

And I found that $$f ^{1}(x)= x^3-4x$$
which can also be factored out as such
$$x(x-2)(x+2)$$

Then you have intervals
$$(-\infty,-2), (-2,0), (0,2),(2,\infty)$$

My question is, with just that is there a way to figure out whether or not the derivative of the function will be greater/less than zero for the respective intervals?

anonymous · Answer

@jim_thompson5910 @ganeshie8 @Ghostgate @satellite73 @nincompoop @mathstudent55

anonymous · Answer

@kropot72

anonymous · Answer

I won't be able to help with this kind of question.

anonymous · Answer

plug in a value and 'test' the derivative at points other than the endpoints of those intervals.

anonymous · Answer

the sign of the derivative remains the same throughout the interval, so all you have to do is plug in a point

anonymous · Answer

I was doing that earlier but I kept getting a negative number when it was supposed to be a positive interval according to webassign, so I was getting all confused...but it turns out that I'm not crazy...I just wrote my derivative wrong lol

anonymous · Answer

Thanks for confirming it anyway