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

Gradient function

Extracts from this document...

Introduction


My coursework on the gradient function is to investigate the gradient on different points on the line and curves.

I will start of my investigation with y = x2. This will be a parabolic curve and the gradient will move from point to point. I will need to start of with a fixed point. I have chosen (2, 4). I will use a table to get close to the point. My table will have five columns. The first column will be x, which will have any numbers between 1and 3. The second column will be y, which will be the result of squaring an x numeral. The third column will be the increase in y, where squared value gets subtracted from 4. The fourth column will be the increase in x, this is where the x values get subtracted from 2. The fifth and last column will be the gradient, where the change in y divided by the change in x, gives me the results. I will do different fixed points so the numbers will vary.

...read more.

Middle

21.6

2.5

25

-11

-0.5

22

2.6

27.04

-8.96

-0.4

22.4

2.7

29.16

-6.84

-0.3

22.8

2.8

31.36

-4.64

-0.2

23.2

2.9

33.64

-2.36

-0.1

23.6

2.99

35.7604

-0.2396

-0.01

23.96

2.999

35.976

-0.023996

-0.001

23.996

3

36

0

0

0

3.0001

36.0024

0.00240004

0.0001

24.0004

3.001

36.024

0.024004

0.001

24.004

3.01

36.2404

0.2404

0.01

24.04

3.1

38.44

2.44

0.1

24.4

3.2

40.96

4.96

0.2

24.8

3.3

43.56

7.56

0.3

25.2

3.4

46.24

10.24

0.4

25.6

3.5

49

13

0.5

26

3.6

51.84

15.84

0.6

26.4

3.7

54.76

18.76

0.7

26.8

3.8

57.76

21.76

0.8

27.2

3.9

60.84

24.84

0.9

27.6

3.99

63.6804

27.6804

0.99

27.96

3.999

63.968

27.968004

0.999

27.996

4

64

28

1

28

Power: 2

Coefficient: 2

Fixed point: 3

My second fixed point is 5, 100

x

y

increase in y

increase in x

gradient

4

64

-36

-1

36

4.1

67.24

-32.76

-0.9

36.4

4.2

70.56

-29.44

-0.8

36.8

4.3

73.96

-26.04

-0.7

37.2

4.4

77.44

-22.56

-0.6

37.6

4.5

81

-19

-0.5

38

4.6

84.64

-15.36

-0.4

38.4

4.7

88.36

-11.64

-0.3

38.8

4.8

92.16

-7.84

-0.2

39.2

4.9

96.04

-3.96

-0.1

39.6

4.99

99.6004

-0.3996

-0.01

39.96

4.999

99.96

-0.039996

-0.001

39.996

5

100

0

0

0

5.0001

100.004

0.00400004

0.00010

40.0004

5.001

100.04

0.040004

0.001

40.004

5.01

100.4004

0.4004

0.01

40.04

5.1

104.04

4.04

0.1

40.4

5.2

108.16

8.16

0.2

40.8

5.3

112.36

12.36

0.3

41.2

5.4

116.64

16.64

0.4

41.6

5.5

121

21

0.5

42

5.6

125.44

25.44

0.6

42.4

5.7

129.96

29.96

0.7

42.8

5.8

134.56

34.56

0.8

43.2

5.9

139.24

39.24

0.9

43.6

5.99

143.5204

43.5204

0.99

43.96

5.999

143.952

43.952004

0.999

43.996

6

144

44

1

44

Power: 2

Coefficient: 2

Fixed point: 5

My third fixed points : 7, 196

x

y

increase in y

increase in x

gradient

6

144

-52

-1

52

6.1

148.84

-47.16

-0.9

52.4

6.2

153.76

-42.24

-0.8

52.8

6.3

158.76

-37.24

-0.7

53.2

6.4

163.84

-32.16

-0.6

53.6

6.5

169

-27

-0.5

54

6.6

174.24

-21.76

-0.4

54.4

6.7

179.56

-16.44

-0.3

54.8

6.8

184.96

-11.04

-0.2

55.2

6.9

190.44

-5.56

-0.1

55.6

6.99

195.4404

-0.5596

-0.01

55.96

6.999

195.944

-0.055996

-0.001

55.996

7

196

0

0

0

7.0001

196.0056

0.00560004

0.00010

56.0004

7.001

196.056

0.056004

0.001

56.004

7.01

196.5604

0.5604

0.01

56.04

7.1

201.64

5.64

0.1

56.4

7.2

207.36

11.36

0.2

56.8

7.3

213.16

17.16

0.3

57.2

7.4

219.04

23.04

0.4

57.6

7.5

225

29

0.5

58

7.6

231.04

35.04

0.6

58.4

7.7

237.16

41.16

0.7

58.8

7.9

249.64

53.64

0.9

59.6

7.99

255.3604

59.3604

0.99

59.96

7.999

255.936

59.936004

0.999

59.996

8

256

60

1

60

Power: 2

Coefficient: 2

Fixed point: 7

The gradient function for y = 2x2  is definitely m = 4x because the x values are four times smaller than the gradients. E.g. my x numeral is -7 and my gradient is -28, if I divide them I get 4.

...read more.

Conclusion

y = 4x. abandoned

My gradient function for y = 4x2  is 4x because if you the tables you will see that the gradients are four times bigger than there x values, an example of this x value -3 and gradient -12 as you can see -3 goes into -12 four times making the gradient function y = 4x.

My conclusion for y = x4  is gradient function is y = 3x2 .I got to this answer by noticing that my gradients for my x numerals were double but then I saw that the gradient was also three times larger than the x value also so at the end the slope must be y = 3x2 .

I can also predict the gradient function for y = x 5 .

Using this table I can predict that y = x^5 is gradient function y = 5x^3. As you can see 2 is the x value and the gradient is 40. To get to 40, you’ll need to cube the 2 and times by five and there you have your answer.

...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)

    found the relationship, but in the end I noticed that for this range of graphs y=ax� the gradient function will be m=3ax�. I think that this is enough research to find a relationship between these three ranges of graphs and their gradients.

  2. The Gradient Function

    This simply means that the gradient of the tangent at x=-1 will be -4. I have also spotted a pattern in the curve of y=2x2. As you can see from the previous results of this curve, when the tangent is at x=1, the gradient has been discovered as 4.

  1. Maths Coursework - The Open Box Problem

    22 9196 20 20 20 8000 Looking at the table you can see that the values do not keep increasing as the length of the cut out increase. I zoomed in on the 10 to 11 region to obtain a more accurate result for the cut out.

  2. Gradient Function

    0.01 35.97 5.999 107.964 0.035997 0.001 35.997 6 108 0 6.001 108.036 -0.036003 -0.001 36.003 6.01 108.3603 -0.3603 -0.01 36.03 6.1 111.63 -3.63 -0.1 36.3 6.2 115.32 -7.32 -0.2 36.6 6.3 119.07 -11.07 -0.3 36.9 6.4 122.88 -14.88 -0.4 37.2 6.5 126.75 -18.75 -0.5 37.5 6.6 130.68 -22.68 -0.6 37.8

  1. The Gradient Function

    and found that the gradients were the same as I thought they would be so this gradient function 20x clearly works showing that gradient function for ax2 is right. For the curve y=x3, the gradient function would be 2x so the gradients of certain points are:- Tangent at x 1

  2. The Gradient Function

    I have also used markings on the tangents such as L1, L2 and L3, which represent line1, line2 etc. I have marked them as such so that it is easier to understand for what point the gradient is. The generalisations of the gradients will be done after the increment method,

  1. The Gradient Function

    the difference between each number, and then work out how far off the first number is: 2 4 6 8 10 +2 +2 +2 +2 The difference between the numbers is 2, and the first number is 2, so I now know that the nth term is 2n.

  2. The Gradient Function

    about this is that as the co-ordinates increase, so does the gradient. Another visible thing is that as the difference between the co-ordinates increases the smaller the increase in the gradient. This method I have used for attaining these results is inaccurate.

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