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Instantaneous Rate of Change Mathematical Investigation

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To discuss initially the average rate of change of a curve, the method of calculating this change of slope can be explored using the provided formula,(f(a+h)-f(a))/h. This will then lead onto the nature of derivatives and the relationship between a function and its derivative.

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Instantaneous Rate of Change Mathematical Investigation
Topics this document covers:
Mathematical analysis Mathematics Analysis Functions and mappings Differential calculus Analytic geometry Derivative Rates Limit of a function Tangent Slope Generalizations of the derivative
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Topics this document covers:
Mathematical analysis Mathematics Analysis Functions and mappings Differential calculus Analytic geometry Derivative Rates Limit of a function Tangent Slope Generalizations of the derivative
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This will then lead onto the nature of derivatives and the relationship between a function and its derivative. This formula works to calculate an average slope of a curved line and works very similarly to ∆x ∆y = slope formula we which calculates the slope treat ∆y or y 2 − y 1 as f(a of a straight + h) − f(a) line and in reference to the ∆x or x 2 − x 1 as h. origin. In this This relationship can be shown on a graph to explore fully how this works. Figure 1 displays the appropriate expression for the coordinates used to calculate the chord and thus the average rate of change of the shown curve. As seen in Figure 1, the average slope between points A and B is shown as the slope between A = (a...
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