Find Function when the derivative exists (Calculator Problem)

I'm looking for help to determine what I should do with my graphing calculator to satisfy the following criteria:

Use a graphing calculator to find f'(2), f'(16), and f'(-3) for the following [functions] when the derivative exists.

The problem I'm currently working on has the function f(x) = 6x²-4x

I am not looking for the answer, but I do want to know how I can determine whether or not the functions' derivative exists, and what I need to do on the graphing calculator.
I do not have any work to support this, because I have no idea where to start.

schuettingerj said:

I'm looking for help to determine what I should do with my graphing calculator to satisfy the following criteria:

Use a graphing calculator to find f'(2), f'(16), and f'(-3) for the following [functions] when the derivative exists.

The problem I'm currently working on has the function f(x) = 6x²-4x

I am not looking for the answer, but I do want to know how I can determine whether or not the functions' derivative exists, and what I need to do on the graphing calculator.
I do not have any work to support this, because I have no idea where to start.

Click to expand...

Do you have the user's manual of your graphing calculator? Look it up....

Since we do not have your calculator, we would not know how this can be accomplished!!

You would know that the graph of this function f(x) = 6x²-4x is a parabola. This function and its derivative are defined for all values of x.

On a GC there are generally two ways to determine the gradient (ie the value of f'(x)) at any point.

One is in GRAPH mode by graphing the function for a relevant domain, tracing along the curve or choosing and x-value, and reading off the value of dy/dx at the point you want. (On a Casio you need to make sure "derivative" is turned on in the setup menu.)

The second way is to use the correct syntax in RUN mode without graphing (depends on GC how you do this - on a Casio input d/dx(6x²-4x,2) to find f'(2)).

(You should also be able to do this manually, and that's a good way to quickly check your results!)