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The Gradient Function


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The Gradient Function

... The Gradient Function Aim: To find the gradient function of curves of the form y=axn. To begin with, I should investigate how the gradient changes, in relation to the value of x. Following this, I plan to expand my investigation to see how the gradient changes, and as a result how a changes in relation to this. Method: At the very start of the investigation, I shall investigate the gradient at the values of y=xn. To start with, I shall put the results in a table, but later on, as I attempt to find the gradient through advanced methods, a table may be unnecessary. As I plot the values of y=x2, this should allow me to plot a line of best fit and analyze, and otherwise evaluate, the relationship between the gradient and x in this equation. I have begun with n=2. After analyzing this, I shall carry on using

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"A substantial piece of work. The development from basic techniques for estimating the gradient through to a proof for deriving the gradient. Plenty of examples were given to illustrate the differences in accuracy between the methods. Further investigation into different cases of the general formula were enlightening, and ultimately fruitful. When used, graphs were a helpful tool in promoting understanding, for instance when illustrating the tangent method. The formatting of the document at times lead at times to the non-prose sections being difficult to read, but this is only a minor concern. Excellent. TSR user: Edenr."
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