Question

limit problem

Answer 1

\[\frac{ f(x)-f(a) }{ x-a }\]

Answer 2

limit as x approaches a

Answer 3

I know this basically represents f'(a)

Answer 4

but I am being asked to use the limit definition to show
f(x)=-x^2-4x+1 at x=-1

Answer 5

ok I know f ' (-1) = -2

Answer 6

but I am not sure what to do with the limit definition

Answer 7

\[\lim x \rightarrow a \frac{ -x^2-4x+1-(-a^2-4a+1) }{ x-a}\]

Answer 8

Is factorization possible?

Answer 9

I don't think so because -x^2-4x+1 looks prime to me

Answer 10

wait maybe factoring by grouping

Answer 11

Yeah that was what I was thinking.

Answer 12

(x-a) seems to cancel out.

Answer 13

-x^2-4x+1+a^2+4a-1
-x^2-4x+a^2+4a note +1-1 cancel out

Answer 14

-(x^2-a^2)=-((x-a)(x+a))

Answer 15

yes I need to regroup them, sorry I am working on paper

Answer 16

-4(x-a)

Answer 17

(x-a) cancels out. Rest is easy :)

Answer 18

ok then I end up with -2a-4 do I then evaluated at a=-1 when then gives me -2(-1)-4=-2 which checks out

Answer 19

Thanks for your help

Answer 20

yw :)