Question

calculus: how do i know if it's relative minima or relative maxima?

Answer 1

http://www.themathpage.com/acalc/max.htm
hope this helps

Answer 2

thank you! :D

Answer 3

You probably know a relative min or max happen at slope of zero, since that's when the curve is flat. But how do you distinguish them? Let's just look at a simple case: Imagine yourself walking along the parabola \(y=x^2\). On your way to the minima, your slope is negative, since you're moving down, but when you're at the minima, of course your slope is zero. Then you keep following the curve and notice your slope has become positive now.

So what's changing here? The slope was negative then zero then positive, so really the slope is what is continually increasing, this is what tells us we went through a minima. So the second derivative has to be positive at the minima for us to know that it is a minima.