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The Gradient Function
Member rating: No Rating | Words: | Submitted: Sat Aug 30 2003
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The Gradient Function The aim of this investigation is to try and find a formula to determine the gradient of a curved line (of the form Y=X^n) at any given point. To do this I have drawn the graph Y=X^2, marked on the tangents and from there calculated the gradients. I have labelled the tangents a-d. I then calculated the gradients by dividing the height of the tangent by the length of the base. A. 2.1 / 1.05 = 2 (gradient) B. 3.9 / 1.05 = 3.7 (gradient) C. 4.2 / 0.75 = 5.6 (gradient) D. 5 / 0.6 = 8.3 (gradient) Y=X^2 X Y Height Base Height / Base A 1 1 2.1 1.05 2 B 2 4 3.9 1.05 3.7 C 3 9 4.2 0.75 5.6 D 4 16 5 0.6 8.3 I then used this same method to find the gradients of tangents on lines other than Y=X^2. I drew a graph for Y=X^3 and used the same method to find the gradients. I came up with these results: Y=X^3 X Y Height Base Height / Base A 1 1 10 2.7 3.7 B 2 8 15 1.2 12.5 C 3 27 27 1.05 25.7 D 4 64 27 0.6 45 You can see that these results are adequate estimate numbers...
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