Investigate the relationship between the gradients of tangents on the curves of graphs, such as y=x2.

... Taha Jamil Ahmad 11AKH (Miss. Pritchard) Gradient Function Coursework My task is to investigate the relationship between the gradients of tangents on the curves of graphs, such as y=x2. To do this, I will first find the gradient of tangents on the graph y=x2 by drawing the graph. I have labelled the tangents a-g. They go from x=-3 to x=4. Below are the calculations for their gradients. (I am using the formula (y2-y1)/(x2-x1) to calculate the gradient of the line. a= (12-6)/(-3.5--2.5) = 6/-1 = -6 b= (6-2)/(-2.5--1.5) = 4/-1 = -4 c= (2-0)/(-1.5--0.5) = 2/-1 = -2 d= (2-0)/(1.5-0.5) = 2/1 = 2 e= (6-2)/(2.5-1.5) = 4/-1 = 4 f= (12-6)/(3.5-2.5) = 6/1 = 6 g= (20-12)/(4.5-3.5) = 8/1 = 8 As you can see, the results I have obtained are good round numbers. These results however are not accurate to the tangents I drew on the graph. There is always going to

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