Finding the derivative at x on a graph

[Kevin011]

Having a hard time figuring out how to estimate the slope of a specific point on a line. Using the graph below, I'm trying to find the derivative of the function f(x) at x = -2, -1, 0, 1, 2, 3, 4, 5


The text book gave me the answers, I just can't seem to figure out how it is estimating the slopes besides pure guessing. These are the answers it gives:

x	-2	-1	0	1	2	3	4	5
Derivative at x	6	2	-1	-2	-2	-1	1	4

I tried estimating the y-coordinates at the given x-coordinates then estimating another point near that point, but I don't seem to be getting a slope anywhere near what they have.
For example:
(-2, 0) and (-1.5, 1.5)
gives a slope of 3

I'm sure this is really simple, so if someone could please shed some light on this for me I would be much apprieciated.

 

[Kevin011]

anyone know how to answer this?

 

[Downtrodden4]

Hope this Helps

Generally when it requires the derivative of a function such as this, the question generally provides some sort of equation. Without that equation the slopes that you require would have to be measured using a ruler and guessing slope of the curve.

ALSO: The slope that you were trying to find by dividing the vertical and horizontal changes to find rise over run is not what you are looking for. That form of slope is called a Secant Line because it intersects the curve twice. The goal of the Derivative is a Tangent line, which only touches the line at one place. This gives you something called the instantaneous slope. It is NOT the same as (Change in y)/ (Change in X) or Rise/Run.

Hope this helps!!!