CALCULUS help please
posted by kunti on .
Find the following limit where f(x) = 4x^2 − 3x.
limit>(f(x+ delta x)f(x))/(delta x)
delta x
**delta x means the triangle symbol with x next to it***

what is delta x approching? if it is approching 0 this is the definition of the derivative. so it will be 8x3. I got this by using the rule that the derivative of ax^n=n*a*x^n1. but they probboly want you to do it without taking the derivative.so lets start by writing it out.
y=delta*x you don't have to do this I just don't want to keep writing delta*x
(4(x+y)^23(x+y)(4x^23x))/(y)
next we want to rewrite this so we can take the limit.
sqrare the x+y
distribute the 4
distribute the 3
get rid of some terms that cancal out and you should get 8*x+4*y3.
now all we have to do is take the limmit as y approches 0.
i get 8x+4*03=8*x3.
this verifys that the derivative of 4*x^23x=8*x3