Question

What does this equation mean?

Answer 1

\[f`(x)=\lim_{h \to 0}\frac{f(x_0+h)-f(x_0)}{h}\]
Or:
\[f`(x)=\lim_{\triangle x \to 0}\frac{f(x_0+\triangle x)-f(x_0)}{\triangle x}\]

Answer 2

We are learning the basics of calculus, and this came up

Answer 3

This is the definition of the derivative. It tells you how to find the slope of the line tangent to the curve f(x) at the point x.

Answer 4

There is much more to it than that however, but that's the basic idea. :)

Answer 5

Check out this video: https://www.youtube.com/watch?v=VOIUtvAdIgs

Answer 6

So, its telling me how to find the slope of a line that hits the curve \(f(x)\) once, at the point \(x\)?

Answer 7

Yes, that is correct!

Answer 8

You can think of the derivative as the "slope of a curve"

Answer 9

So kinda like this?

Answer 10

It's based on the same ideas that you used in algebra to find the slope of a line.

Answer 11

So it gives the slope for that line?

Answer 12

That is close... the long equation is precisely the slope of that line, exactly

Answer 13

Note that it doesn't give you the equation of the ENTIRE line, just the SLOPE

Answer 14

That video I posted explains it in more detail.

Answer 15

It's only about 3 minutes

Answer 16

Oh, K

Answer 17

Yup. But then, since you also know the point where it hits \(f(x)\), couldn't you just sub those values into: \(y-y_1=m(x-x_1)\)?

Answer 18

To find the equation for the line?

Answer 19

Of course, that is considered a more advanced technique called "Linearization" basically figuring out the line that matches the curve at a given point. You've got the idea!

Answer 20

Ok, thanks so much @jtvatsim :D

Answer 21

No problem, and good luck with your studies! :)