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Differential equations

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f(x) = (x^2)sin(1/x)+x if x doesn't equal 0
f(x) = 0 if x=0

Prove that the function f:R-> R is differentiable and that f'(0)=1. Also prove that there is no neighbourhood I of 0 such that the function f:I->R is increasing.

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Solution Summary

This is a proof regarding differentiability of a function.

Solution provided by:
  • BSc, University of Bucharest
  • MSc, Ovidius
  • MSc, Stony Brook
  • PhD (IP), Stony Brook
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