Question

use the definition of derivatives to compute f(x)= 3x-x^2

Answer 1

Show me your best guess and I'll help.

Answer 2

Okay thanks.

Answer 3

\[\frac{ 3(x+h)-(x+h)^{2} -3x-x ^{2}}{ h} \] Is that right so far?

Answer 4

just one error
-(3x-x^2) will be -3x + x^2

Answer 5

after correcting that, you can expand
3(x+h) and (x+h)^2
and notice which terms get cancelled from the numerator.

Answer 6

yes! I just did. That's why I was confused. So far I have \[\frac{ 3h+2xh+h ^{2} }{ h }\]

Answer 7

now what can you factor out from the numerator ?

Answer 8

AND,
shouldn't that be -2xh ??

Answer 9

-(x+h)^2 = -x^2-h^2\(\large -2xh\)

Answer 10

and -h^2 too

Answer 11

ohh I see what I did. so i should always distribute my negatives first?

Answer 12

yes, thats preferable

Answer 13

now tell me what u get as numerator ?

Answer 14

so then i get \[3h-2xh-h ^{2}\]and i factor out the h and get 3-2x-h

Answer 15

absolutely correct!
and since lim h->0
you can now directly plug in h=0 :)

Answer 16

Yay! Thanks so much for your help. You cleared everything up for me !

Answer 17

Don't forget you can check yourself really easily, and you always should, by taking the derivative the easy way!

Answer 18

and whats your final answer ? and yes, cross-checking is always good :)

Answer 19

3-2x

Answer 20

thats correct :)
welcome ^_^

Answer 21

Thanks! :)