Discovering the Gradient Function

Discovering the Gradient Function

The aim of this investigation is to discover the gradient function for

the graphs y = ax where a and n are constants.

I will do this by beginning with the simplest cases, as I believe that

these will be the most simple equations to solve. I am doing this in

the hope that discovering the equations for these simple cases will

aid me in discovering the more complex formulas.

Firstly I will construct the graphs of: y=x, y=2x, y=3x, y=4x. And

attempt to find a general equation.

Y=x

X

1

2

3

4

Y

1

2

3

4

Y=2x

X

1

2

3

4

Y

2

4

6

8

Y=3x

X

1

2

3

4

Y

3

6

9

12

Y=4x

X

1

2

3

4

Y

4

8

12

16

(Graph1)

Using the rule stated on the candidate sheet I can calculated the

gradient for each of the above straight lines.

Equation of line

Gradient Function

Y=x

1

Y=2x

2

Y=3x

3

Y=4x

4

Doing this I have discovered that the co-efficient of x is the

gradient of the line.

I will now go on to construct the graph of y=x2. This is because I

know that the graph of x2 will be a curve and it is curves that I am

investigating

X

1

2

3

4

Y

1

4

9

16

To find the gradient of this line, I will use the tangent method.