Gradient Function Lab Report

The Gradient Function

I am trying to find a formula that will work out the gradient of any line (the gradient function)

I am going to start with the simplest cases, e.g. g=c², g=c, g=c3 etc. as they are probably going to be the easiest equations to solve as they are likely to be less complex and hopefully the formulas to the more complex equations will be easier to discover by looking at the previous formulas.

I am going to look at the line g=c² first.

g=c²

c

1

2

3

4

g

1

4

9

16

Please see graph on separate piece of paper

One of the most obvious things I notice is that as the co-ordinates increase so does the gradient.

I already know the gradient of the line, as you can tell from the equation the gradient is always going to be one as there are always going to be the same values as each other. Below is a sketch of how the line would look.

c

g

Gradient

1

1

1

2

2

1

3

3

1

4

4

1

There is no need to use the small increment method here, as I know that the gradient is accurate as c-c is always going to equal 1. A formula to work out the gradient function for this equation is:

c/c

Which is simple a way of getting to the number 1 which is of course always going to be the answer if the c and g coordinates are the same. Another formula is of course just simple 1.

Now I am going to look at the line g=c³. I predict that this line will look similar to Y=c² but it will be steeper and indeed it is, by entering the two equations into my calculator I can see that the equation g=c³ is steeper than Y=c². Going by the formula for the previous equation I would have thought that the formula for this equation might be 3c.

c

1

2

3

4

g

1

8

g=c-3

c

g

Gradient

1

1

-3

2

0.125

-0.187

3

0.037

-0.037

4

0.0156

-0.011

-3*1-4=-3 -3*2-4=-0.1875 -3*3-4=-0.037 -3*4-4=-0.011

As you can see the formula does work, this means that the formula will obviously work for more complex equations e.g. g=2c-3+5c-2 + 902c-324. To work these out you would split up the equations as I explained earlier.

You can get equations like y=3X and y=128X14 you can work these out using the formula nx(n-1).To work these out, I will take for example y=128X14 you first work out y=X14 and then you times it by 128, which makes sense as it is 128 lots of X14.

To work out slightly more complex equations such as g=2c3+5c2, all you do is use the equation nx(n-1) but break up the equation into two so you have two equations, take for example g=2c3+5c2 you would break it up to g=2c3 and g=5c2 . Then you work out the equations as normal as shown below.

g=2c3

c

Gradient

1

6

2

24

3

54

4

96

g=5c2