• Join over 1.2 million students every month
  • Accelerate your learning by 29%
  • Unlimited access from just £6.99 per month

The Gradient Function

Extracts from this document...

Introduction

The Gradient Function

x=a’ is a vertical line which intercepts the x-axis at point ‘a’.

‘y=a’ is a horizontal line which will intercept the y-axis at point ‘a’.

‘y=ax’ and ‘y=-ax’ are the equations for a sloping line which intercepts at the origin. The value of ‘a’ is the gradient of the line, so therefore the larger the value of ‘a’ the steeper the gradient of the line.

I am trying to find the gradient function this is a formula that will work out the gradient of any line.

...read more.

Middle

x

-3

-2

-1

0

1

2

3

x2

9

4

1

0

1

4

9

y

9

4

1

0

1

4

9

(See graph, fig.1)

From the graph we can see that as the values of the coordinates increases, so does the gradient. We can see this from the

...read more.

Conclusion

‘y’ value’s by squaring the ‘x’ value. The closer the two points the more accurate the result will be, for example if we choose ‘2’ as the first ‘x’ value we could then choose ‘2.001’ as the next ‘x’ value. The gradient is found using the equation:

Gradient=y1-y2

                                                     x1-x2

So using the example numbers from above I would find the gradient as shown below:

Gradient=y1-y2

                                                     x1-x2

=4.004001-4

2.001-2

Gradient =4.001

This method is more accurate than using the results from the graph. This is because when taking results from the graph it is very difficult to get them as precise.

...read more.

This student written piece of work is one of many that can be found in our GCSE Gradient Function section.

Found what you're looking for?

  • Start learning 29% faster today
  • 150,000+ documents available
  • Just £6.99 a month

Not the one? Search for your essay title...
  • Join over 1.2 million students every month
  • Accelerate your learning by 29%
  • Unlimited access from just £6.99 per month

See related essaysSee related essays

Related GCSE Gradient Function essays

  1. Peer reviewed

    The Gradient Function Coursework

    5 star(s)

    The following equation denotes this: dy ?y dx ?x By finding dy / dx from y I used a procedure called differentiating y with respect to x. The gradient function I developed is indeed a generally used function in calculus, and this backs up the findings of this assignment.

  2. Gradient function

    3220.776 9.7 8852.928 2291.9281 0.7 3274.183 9.8 9223.682 2662.6816 0.8 3328.352 9.9 9605.96 3044.9601 0.9 3383.289 9.99 9960.06 3399.05996 0.99 3433.394 9.999 9996.001 3435.0006 0.999 3438.439 10 10000 3439 1 3439 Power: 1 Coefficient: 4 Fixed point: 9 Conclusion My conclusion for y = x2 is that the gradient function is y = 2x.

  1. Gradient Function

    Using this information I can conclude that the gradient on any point on that curve will be the cubed value of X. Therefore the gradient on this is m=3X 2 Using differentiation for Y=X3, I can write this gradient as dy dx Y=3X2 +5x My first fixed point is 3,

  2. The Gradient Function

    I know that this gradient function 3ax2 only works for y=ax3 graphs as the gradient function for y=ax2 that we found before doesn't work for any other y=axn graphs. This means I don't need to test the gradient function 3ax2 on any other graphs like y=ax4 graphs For the curve

  1. The Gradient Function

    where I will compare the tangents obtained by the increment method and the tangent method. Graph: Y= 1/x The table below shows the points, which I have used to plot the graph X Y -4 -0.25 -2 -0.5 -1 -1 -0.5 -2 0.5 2 1 1 2 0.5 4 0.25

  2. The Gradient Function

    G = y1-y2 x1-x2 G = 10.001 G = 10 For point x=6: y1 = 62 y1 = 36 x2 = 6.001 y2 = 6.0012 y2 = 36.010001 G = y1-y2 x1-x2 G = 12.001 G = 12 To work out the pattern of these numbers, I can look for

  1. The Gradient Function

    I am once again going to substitute the values into the equation. . The Change in Y = 1 = 3.3 The Change in X = 0.3 As you can see, this isn't exactly the most accurate answer either. If you calculate it correctly, -0.5 x 6 = -3.

  2. The Gradient Function Investigation

    y = 3x� Gradient = 3(x + h)� - 3x� (x + h) - x = 3(x + h)(x� + 2xh + h�) - 3x� (expand brackets) h = 3(x� + 3x�h + 3xh� + h�) - 3x� (expand and simplify) h = (3x� + 9x�h + 9xh� + h�)

  • Over 160,000 pieces
    of student written work
  • Annotated by
    experienced teachers
  • Ideas and feedback to
    improve your own work