How to get instantaneous rate of change

[Maroc]

Homework Statement

6x^2 - 4
x = -2

Homework Equations

n/a

The Attempt at a Solution

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

 

[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?

 

[Maroc]

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?

Thanks a lot Bohrok. I got it :shy:

 

[Maroc]

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?

i know how to use it but not why.

 

[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.

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

Although this is precalc, this page should help you understand it all
http://en.wikipedia.org/wiki/Derivative

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

 

[Maroc]

oh thanks Bohrok. I know have a better understanding.

 

[charliemagne]

Homework Statement

6x^2 - 4
x = -2

Homework Equations

n/a

The Attempt at a Solution

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

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.