Thread: critical points - maximum, minimum, or point of inflection?

Ok so I get how to find the critical points but I don't understand how you tell if it's mmaximum, minimum, or point of inflection. Say I have one point (-2,-16), what would it be?

Originally Posted by needprecalchelp

Ok so I get how to find the critical points but I don't understand how you tell if it's mmaximum, minimum, or point of inflection. Say I have one point (-2,-16), what would it be?

You'll have to excuse me, but my mind-reading ability is slipping terribly. Would it be too much to ask you to provide a bit more information about the function that generates the value f(-2) = -16 ?

One more small item ... you understand that determining what you want answered will most probably require analysis using the second derivative, a calculus topic?

no this is from precalc class. The original question is f(x) = x^2 + 4x -12 and I'm supposed to find the critical points for the function and determine whether each point is a maximum, minimum, or point of inflection. I found the critical point to be (-2,-16).

Originally Posted by needprecalchelp

no this is from precalc class. The original question is f(x) = x^2 + 4x -12 and I'm supposed to find the critical points for the function and determine whether each point is a maximum, minimum, or point of inflection. I found the critical point to be (-2,-16).

note that the graph of f(x) is a parabola that opens upward ... what does that tell you?

That it's minimum. But how can I find out without graphing?

Originally Posted by needprecalchelp

That it's minimum. But how can I find out without graphing?

I don't understand ... knowing that the graph of f(x) is a parabola is basic knowledge.

If you can't use that information, then you would need to use calculus.