# How to get instantaneous rate of change

1. Sep 26, 2009

### Maroc

1. The problem statement, all variables and given/known data
6x^2 - 4
x = -2

2. Relevant equations
n/a

3. The attempt at a solution

I input -2 for x but i got the wrong answer..the answer is suppose to be -24

2. Sep 26, 2009

### Bohrok

You'll need to use the difference quotient
$$\frac{f(x + h) - f(x)}{h}$$

Do you know why and how to use it for the problem?

3. Sep 26, 2009

### Maroc

Thanks a lot Bohrok. I got it :shy:

4. Sep 26, 2009

### Maroc

i know how to use it but not why.

5. Sep 26, 2009

### Bohrok

The slope m between two points (x, f(x)) and (x1, f(x1)) is given by the following, which you should be familiar with:

$$m = \frac{f(x_1) - f(x)}{x_1 - x}$$

To make it easier to work with, let x1 = x + h, so h is basically the distance between the x values of the two points.

$$m = \frac{f(x + h) - f(x)}{x + h - x} = \frac{f(x + h) - f(x)}{h}$$

http://en.wikipedia.org/wiki/Derivative

Look especially at the secant lines where you let h go to 0.

6. Sep 26, 2009

### Maroc

oh thanks Bohrok. I know have a better understanding.

7. Sep 26, 2009

### charliemagne

The easier way that I know is that you have to find the derivative of f(x) = 6x^2 - 4.

Then substitute -2 to x.

Note: Use the easier way in finding derivatives.