f(x)=6*x^2-x
f(x+h)-f(x)/h
Solve the Function. (Show your work please)

Question

turingtest · Answer

ugh.. these things are a pain to type out but I'll try. Wait do you need the limit as h-->0 or just the "f(x+h)-f(x)/h" part?

anonymous · Answer

in my prob it says that H does not equal to zero

anonymous · Answer

U still there?

turingtest · Answer

good, no limits then$$f(x)=6x^2-x$$$$f(x+h)=6(x+h)^2-(x+h)=6x^2+12xh+h^2-x-h$$$$f(x+h)-f(x)=6x^2+12xh+h^2-x-h-(6x^2-x)$$$$=12xh+h^2-h$$$$[f(x+h)-f(x)]/h=(12xh+h^2-h)/h=12x+h-1$$

turingtest · Answer

sorry takes a while to write it out

anonymous · Answer

no you're fine... i was just checking.

turingtest · Answer

PS in the future you want to write this as
[f(x+h)-f(x)]/h
the brackets are important to show that everything is over h, not just the f(x) part

anonymous · Answer

my bad. not the brightest crayon in the box when it comes to math. haha

turingtest · Answer

well if you got to precalculus (that's what this is right?) then you're doing fine. Parentheses can be tricky when writing on this site

anonymous · Answer

so the answer is 12x+h-1? If it is, my hw site is saying that it's wrong.

turingtest · Answer

sorry I lost a 6 it should be
12x+6h-1

turingtest · Answer

If this was calculus that would not have mattered, that's why I ignored it

turingtest · Answer

f(x)=6x^2−x
f(x+h)=6(x+h^)2−(x+h)=6x^2+12xh+6h^2−x−h
f(x+h)−f(x)=6x^2+12xh+6h^2−x−h−(6x^2−x)
=12xh+6h^2−h
[f(x+h)−f(x)]/h=(12xh+6h^2−h)/h=12x+6h−1
is how it was supposed to be

anonymous · Answer

yeah, it was the 6. this is college algebra btw.

turingtest · Answer

Oh, well FYI they are giving you this because it is essential to the definition of the derivative, which is
$$\lim_{h \rightarrow 0}[f(x+h)-f(x)]/h$$you may not have done limits yet but you can see that if h was zero you would get
12x-1
whether the "h" had a 6 in front or not.

anonymous · Answer

Yeah, we just began doing these...