Question

find the slope of the curve at y=1/x-1

Answer 1

What's the curve?

Answer 2

It doesn't give it, you'd have to graph it

Answer 3

i'm really confused..

Answer 4

If this is calculus, it is probably referring to the tangent curve...

Answer 5

In which case it would be the derivative of the function

Answer 6

this is most definitely calculus, but I plugged it in to the f(x+h) - f(x) all over h formula

Answer 7

and ended up with 1/h^2 and I'm really confused..

Answer 8

You haven't learned the derivative formulas yet??? It is much shorter

Answer 9

what derivative formulas?!

Answer 10

fml

Answer 11

ok so ther derivative of 1/x= x^-1=x^-2 = 1/x^2. The derivative is one over x squared which is the slope

Answer 12

how does x^-1 = x^-2? what?

Answer 13

That is from the formula for derivatives of x to a power. you -1 from the power which in this case makes it x^-2

Answer 14

I don't see how it makes it x^-2 and in the back of the book the answer says -1/(x-1)^2

Answer 15

Lol. If you haven't learned the derivative formulas you have to do it the hard way and use the definition.

Answer 16

could you please show me how to do it the definition way?

Answer 17

or if i show you my work will you tell me what I did incorrectly?

Answer 18

Ok

Answer 19

that is really what it says in the back of the book?!

Answer 20

yes! i've tripple checked, i'm assuming it's wrong

Answer 21

no wonder people get confused
\[-\frac{1}{(x-1)^2}\] is not the slope of anything

Answer 22

it is a FORMULA for the slope of the line tangent to the curve
you need to know \(x\) to find an actual slope

Answer 23

they don't ask for that though, so no idea why it's in the back of the book.. jvioejiwoeajfiewao

Answer 24

it is not wrong in the sense that \(-\frac{1}{(x-1)^2}\) is not the formula for the slope, and we can find that if you like

Answer 25

can you check my work for me? i'm using the derivative function because we havn't learned any formulas

Answer 26

so you are working directly from the definition, right?

Answer 27

\[\lim_{h\to 0}\frac{f(x+h)-f(x)}{h}\] is what i assume you are using

Answer 28

yes! and it ended up like this..

Answer 29

a word of advice before you start
1) is a only algebra, but you have to do it carefully
2) work step by step, and ignore the \(h\) in the denominator until all the algebra is done in the numerator

Answer 30

but then i simplified the numerator