Review in calc I to prepare for calc II

[ranger]

I'm doing a review in calc I to prepare for calc II. I'm now applications of derivatives (optimization). Okay so when I have the function I need to optimize, I need to take the derivative and find the critical point of the first derivative. But sometimes there's more than one critical point. Is there any sort of test that I can do to find which critical point I should use.

--thank you.

 

[Mindscrape]

Why not a first derivative test? I assume you have done one before. If the derivative is negative until the critical point, then positive after the critical point then you have a maximum. The other way around for a minimum. Essentially limits with derivatives.

 

[ranger]

Ah the first derivative test. Thanks for the input.

 

[d_leet]

Why not a first derivative test? I assume you have done one before. If the derivative is negative until the critical point, then positive after the critical point then you have a maximum. The other way around for a minimum. Essentially limits with derivatives.

Other way around, if the derivative is negative to the critical point and the positive after the value at that point is a minimum, because the function decreases to that point and then increases.

 

[Demian^^]

You could also get the second derivative and evaluate it in the critical points (where the first derivative is zero). If the second derivative is negative you have a maximum, if it's positive you have a minimim and if it's zero you have (what i directly translate from dutch, because I don't know what it's called in english) a bending point, as you would have in the function y=x^3. If calculating the second derivative isn't too much work, I generally use this method to establish the nature of a critical point.