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Calculus Mathematical Investigation

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The instantaneous rate of change describes the rate of change at a particular point. For a function, the instantaneous rate of change at that point is equal to the slope of the tangent line at the point. Investigation explores concepts such as first principles and exploration of power rule.

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Calculus Mathematical Investigation
Topics this document covers:
Mathematical analysis Mathematics Analysis Functions and mappings Differential calculus Differentiation rules Derivative Rates Limit of a function Graph of a function Tangent Calculus
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Topics this document covers:
Mathematical analysis Mathematics Analysis Functions and mappings Differential calculus Differentiation rules Derivative Rates Limit of a function Graph of a function Tangent Calculus
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Mathematical Investigation- Instantaneous Rate of Change Introduction: The instantaneous rate of change describes the rate of change at a particular point. For a function, the instantaneous rate of change at that point is equal to the slope of the tangent line at the point. Instantaneous rates of changes of functions are important to study, as the functions can be used to describe the rate of change of various systems, including the resistance to the flow of electricity in metals, costs of production, crystal growth and motion in a straight line. In Part A, the instantaneous rate of change will be approximated and calculated with the function of f(x) = x2 while in Part B will be calculated with the function g(x) = x4. In Part C a generalized conjecture will be made for the derivatives with other powers of x with respect to x of xn. Part A- The Instantaneous Ra...
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