I'm taking AP Calc AB this year and this is a question I've come across while doing work on my own and I won't be seeing my teacher for a few days, so I' figured I'd ask some of you guys. Let's say you have an equation f(x)=(x^3)+(5x^2) and you need to find the relative minimum of that function. Take the derivative and set it to zero to find where the slope levels off, but how do you know which of the two x values gives the minimum? Is it a common sense type thing, because I know that with such a simple function you can deduce that, because it's a positive cubic function, the maximum will come first, and so naturally the minimum will be the larger x value, but is there a more mathematical way to do this? Thanks in advance. Just kidding, I found out how to do it. Pretty easy.