Gradient function

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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.

I will then do other functions such as Y=4x2

Next I will move to a function y = x4  and investigate the gradient at different points.  I will use the same method used in the equation

y = x2 but instead of squaring the numbers I will cube them.

After my investigating finishes I will come up with a conclusion which will summarize my investigation.

y=x2

My first fixed point is 2, 4


Power: 2

Coefficient: 1

Fixed point: 2

My second fixed point is 5, 25

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Power: 2

Coefficient: 1

Fixed Point: 5

My third fixed point is -3, 9

Power: 2

Coefficient: 1

Fixed point: -3

From looking at my tables I can see that my gradient is two times bigger than my x value. An example of this is when x is 10, the gradient is 20 and if I divide them I get 2. Another example of this is when my x is 2, the gradient is 4 and if you divide them you get 2. This proves that my gradient is m = 2x. If ...

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