Question

Function question! Help please?

Answer 1

For f(a+b) you replace x with a+b in the formula.
For f(a) you replace x with a in the formula.
You plug them in and do the calculations.

(If the desired expression was
\[\lim_{b \rightarrow 0} \frac{f(a+b)-f(a)}{b}\]
then the result would be f'(a), that is the derivative of f(x) for x=a.)

Answer 2

so my next step would be \[(a+b)^2 - 5(a+b) + 6 + a^2 - 5a +6\]

and would it all be over b?

Answer 3

yes

Answer 4

but the 2nd part is subtracted... you are adding

Answer 5

so then i would have \[\frac{ a^2 + 2ab + b^2 - 5a - 5b + 6 - 2a + 5a + 6 }{ b }\]

Answer 6

you want the top to be
\[ (a+b)^2 - 5(a+b) + 6 -( a^2 - 5a +6)\]

Answer 7

whoops I meant \[-a^2\] not 2a

Answer 8

and i meant -6 not +6

Answer 9

Okay so once I have all that correct, what do I do? Do I simplify?

Answer 10

yes, collect terms, then divide out the b's

Answer 11

my final answer would be 2a + b - 5

Thanks :) Getting started is the hardest part for me!

Answer 12

yes, looks good.

It appears you are starting to learn calculus

Answer 13

yayy!! Haha thanks again!