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Limit-free derivatives
Published online by Cambridge University Press: 23 January 2015
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Algebraic double roots are used by [1] to motivate the following limit-free definition of derivative:
‘A function f(x) has a derivative m at x = a if
for some value c.’
As we shall see later, ‘function’ in this definition will actually be restricted to real polynomials and [1] concludes
‘We have shown how an elementary algebraic principle — double roots — can lead to a complete calculus of polynomials and related functions, without the need for a limit concept.
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