# General derivative functions

• Jun 27th 2012, 09:32 PM
rortiz81
General derivative functions
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.
• Jun 27th 2012, 09:42 PM
pickslides
Re: General derivative functions
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
• Jun 28th 2012, 08:09 AM
richard1234
Re: General derivative functions
The two definitions are quite similar. Let $x = a+h$ for some small h and you'll see what I mean.
• Jun 28th 2012, 01:45 PM
rortiz81
Re: General derivative functions
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 $g(x)=x^2+3x+2$. I get the same answer when using either method: $2a+3$. However it was easier for me to use the $h\rightarrow0$ method because it didn't require polynomial division like the other one did.

Thank you for all your help.
• Jun 28th 2012, 05:53 PM
richard1234
Re: General derivative functions
They should be the same, or roughly the same...I don't see why one definition would be significantly different from the other.