Gradient Function

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                                Gradient Function

Introduction

   For this project, I will deduce the gradient for several y=axn graphs and with this find any sort of relationships between the x values and the gradient. A gradient is the steepness of a curve at a point. Gradients can prove to be very useful. It usually means something in most graphs for e.g. in distance-time graphs, the gradient indicates the speed. The gradient formula for a straight line is:

Gradient =   Change in y

                      Change in x

   However, since the y=axn forms a curve rather than a simple straight line, it is much more apprehensive to calculate its gradient. Therefore, another method has to be applied. The gradient for the non-linear graph is the steepness of a curve at one particular point. In order to find this, I will need to draw specific tangents on different x-axis points. A tangent in a non-linear graph is a straight line that essentially touches the curve at one point with two tiny alike angles either side. It must not touch more than one particular point or intersect the curve, as this will distort the outcome. As a result, we can say that the curve’s steepness at a particular point is identical to the tangent formed in that specific curve.

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   I will draw four graphs: y=x2, y=x3 y=2x2 and y=x-1. From each of these graphs I will infer different gradients and compare my results with the theoretical result that is found by using the ‘Small Increments Method’. By comparing the two results, I can distinguish if my practical method and theoretical method give similar results that is the steepness of the curve at a given point. I will also try to spot any patterns that may occur.

Theoretical Method

Small increments Method

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There is absolutely no problem with the writing part if we neglect a few typographical errors here and there.

I can strongly say that the student has worked hard on this coursework but his/her method is not completely right. Looking at this work I can suggest that this essay is written slightly on a memorising basis. It is not clear why we can reduce the value of h in all 3 examples to zero and neglect them. Since we are trying to find the gradient at one specific point and not between two points like in a straight line, therefore the value of h MUST be neglected to prevent us from virtually drawing a straight line between two point on a curve and find the gradient of that straight line. Nonetheless the coursework is very useful and deserving of a good grade.

Using 3 different worked examples and explanations is the best part of this coursework which helps the reader completely understand what is being explained here. The student successfully answers the question and provides useful information to justify his answers however they are quite not enough. Using drawn graphs in the coursework would have helped the reader understand the sequence of logic better.