Question

If i use the formula for tangent line approximation

F(x)=f(a)+f'(a)(x-a)

and i use the function x^2 i end up with

F(x)=x^2+2x(x-a)
what would i use for my (x-a)

Answer 1

the smaller your a, the better your approximation

Answer 2

usually, with problems like that, our teacher would ask the error, based on the a used for a given interval

Answer 3

So a can be any number i pick?

Answer 4

it sounds like something is missing from the question to me

Answer 5

Well the goal is to come up with three problems to give to the teacher (don't ask me why) but this is the first time i have ever seen this stuff.

Answer 6

Ok, so linear approximation, is F(x0) + F'(x0)(x-x0), (x-x0) is deltax, or change in x. the smaller the change, the better the accuracy (usually)

Answer 7

maybe you can choose functions whose accuracy changes drastically depending on what delta you choose

Answer 8

it's not really about the a or x0 that you use, but that delta x

Answer 9

Ok thanks man i think i understand now