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Victoria Jennings- 11SEG GCSE Mathematics Coursework 2003 The Gradient Function In this piece of coursework I will investigate the gradient function. The "steepness" of a curve is measured by its gradient. The gradient of a curve at a particular point is defined as the gradient of the tangent drawn to the curve at that point. The gradient at a point on any curve is defined as the gradient function. I will carry out this investigation using the equation: y = axn I am trying to find a formula that will work out the gradient of any line. ...................................................................................................... We can use the "tangent method" to obtain the gradients of graphs of different functions. I am going to look at y=x1 first because it is the easiest. See graph A y -4 -3 -2 -1 0 1 2 3 4 x -4 -3 -2 -1 0 1 2 3 4 As we see, the gradients of y=x is very simple, g=1. We even do not need to draw any tangents to obtain the gradients. So the relationship between g and x can be shown...

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