Use the definition of the derivative to find the derivative of f (x) at the indicated point:
f(x)=x^2-x at x=3

Question

Use the definition of the derivative to find the derivative of f (x) at the indicated point:
f(x)=x^2-x at x=3

kainui · Answer

Show me your best guess or where you get stuck. There's no point in me explaining the entire thing when I'm sure you can do some of it already.

haseeb96 · Answer

f(x)=x^2-x
differentiate w.r.t x 
df(x)\dx= d\dx (x^2 -x)
           by appling power function
d\dx x^n = nx^n-1 
          df(x)\dx    = 2x -1.........eq#1
now put x =3 in eq#1
             =2(3)-1
             = 6-1 
       df(x)\dx      =5

haseeb96 · Answer

this is the correct answer

anonymous · Answer

I am supposed to use:
f ' (x) = ( f (x+h) - f (x) )/ h as h approaches zero

kainui · Answer

Yeah, I don't know what @Haseeb96  is doing, I think he needs a nap. lol

So malibu, you know what to use, show me your steps. I'll help you along, but only if you make an effort and guess.

anonymous · Answer

I think i got it, how to do it. The answer is 5.

anonymous · Answer

But I did it differently. I mean the setup too.

kainui · Answer

You should have done it with the definition, so if you mean you did it differently than Haseeb then yeah, that's great. Otherwise, it's wrong.

anonymous · Answer

Yes I used 
f'(x)=lim h approaches 0 f(x+h)-f(x)/h

haseeb96 · Answer

then put the given x=3 in the given answer

anonymous · Answer

But thanks, @Haseeb and @Kainui.

kainui · Answer

At least you have the quick shortcut to taking the derivative so that you can check yourself! Always check yourself on "definition of a derivative" questions since it's so easy!