... 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 x y change in y change in x gradient 1 1 3 1 3 1.1 1.21 2.79 0.9 3.1 1.2 1.44 2.56 0.8 3.2 1.3 1.69 2.31 0.7 3.3 1.4 1.96 2.04 0.6 3.4 1.5 2.25 1.75 0.5 3.5 1.6 2.56 1.44 0.4 3.6 1.7 2.89 1.11 0.3 3.7 1.8 3.24 0.76 0.2 3.8 1.9 3.61 0.39 0.1 3.9 1.99 3.9601 0.0399 0.01 3.99 1.999 3.996001 0.003999 0.001 3.999 2 4 2.001 4.004001 -0.004001 -0.001 4.001 2.01 4.0401 -0.0401 -0.01 4.01 2.1 4.41 -0.41 -0.1 4.1 2.2 4.84 -0.84 -0.2 4.2 2.3 5.29 -1.29 -0.3 4.3 2.4 5.76 -1.76 -0.4 4.4 2.5 6.25 -2.25 -0.5 4.5 2.6 6.76 -2.76 -0.6 4.6 2.7 7.29 -3.29 -0.7 4.7 2.8 7.84 -3.84 -0.8 4.8 2.9 8.41 -4.41 -0.9 4.9 3 9 -5 -1 5 Power: 2 Coefficient: 1 Fixed point: 2 My second fixed point is 5, 25 x y change in y change in x gradient 4 16 9 1 9 4.1 16.81 8.19 0.9 9.1 4.2 17.64 7.36 0.8 9.2 4.3 18.49 6.51 0.7 9.3 4.4 19.36 5.64 0.6 9.4 4.5 20.25 4.75 0.5 9.5 4.6 21.16 3.84 0.4 9.6 4.7 22.09 2.91 0.3 9.7 4.8 23.04 1.96 0.2 9.8 4.9 24.01 0.99 0.1 9.9 4.99 24.9001 0.0999 0.01 9.99 4.999 24.99 0.009999 0.001 9.999 5 25 5.001 25.01 -0.010001 -0.001 10.001 5.01 25.1001 -0.1001 -0.01 10.01 5.1 26.01 -1.01 -0.1 10.1 5.2 27.04 -2.04 -0.2 10.2 5.3 28.09 -3.09 -0.3 10.3 5.4 29.16 -4.16 -0.4 10.4 5.5 30.25 -5.25 -0.5 10.5 5.6 31.36 -6.36 -0.6 10.6 5.7 32.49 -7.49 -0.7 10.7 5.8 33.64 -8.64 -0.8 10.8 5.9 34.81 -9.81 -0.9 10.9 6 36 -11 -1 11 Power: 2 Coefficient: 1 Fixed Point: 5 My third fixed point is -3, 9 x y change in y change in x gradient -4 16 -7 1 -7 -3.9 15.21 -6.21 0.9 -6.9 -3.8 14.44 -5.44 0.8 -6.8 -3.7 13.69 -4.69 0.7 -6.7 -3.6 12.96 -3.96 0.6 -6.6 -3.5 12.25 -3.25 0.5 -6.5 -3.4 11.56 -2.56 0.4 -6.4 -3.3 10.89 -1.89 0.3 -6.3 -3.2 10.24 -1.24 0.2 -6.2 -3.1 9.61 -0.61 0.1 -6.1 -3.01 9.0601 -0.0601 0.01 -6.01 -3.001 9.006001 -0.006001 0.001 -6.001 -3 9 -2.999 8.994001 0.005999 -0.001 -5.999 -2.99 8.9401 0.0599 -0.01 -5.99 -2.9 8.41 0.59 -0.1 -5.9 -2.8 7.84 1.16 -0.2 -5.8 -2.7 7.29 1.71 -0.3 -5.7 -2.6 6.76 2.24 -0.4 -5.6 -2.5 6.25 2.75 -0.5 -5.5 -2.4 5.76 3.24 -0.6 -5.4 -2.3 5.29 3.71 -0.7 -5.3 -2.2 4.84 4.16 -0.8 -5.2 -2.1 4.41 4.59 -0.9 -5.1 -2 4 5 -1 -5 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 ...

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