The first one gives you the gradient between two points - a linear type profile.
The later can be used to find the gradient at any point on a curve - nonlinear
Hi, I'm starting derivatives and I am getting confused. Some problems seem easier solved by
f(x)-f(a)
---------
x - a
As x approaches a
and some by
f(a+h)-f(a)
-----------
h
as h approaches 0
Why is this and how do I choose the best option? Does it matter if it's a velocity problem and not a tangent problem? I thought they were the same. Does it matter if I have a point (c,f(c)) to go off of? I apologize if I'm not making much sense, but I have practiced both methods and still don't understand why they are different.
Ok. I think I understand. One is a secant line and one is a limit. Right? Or are they both limits? Are these two completely interchangeable? Say I have the function . I get the same answer when using either method: . However it was easier for me to use the method because it didn't require polynomial division like the other one did.
Thank you for all your help.