Continuity
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Maxima and minima
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It is assumed at this stage that the student is familiar with how the first and second derivatives of a differentiable function f determine its maxima and minima. The purpose of this chapter is to develop a more rigorous approach to the theory of turning points of differentiable functions. In a rigorous treatment of the subject theorems proving the existence of maxima and minima depend on certain technical theorems about the values the derivative takes over a closed interval.
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Contents of
Continuity
1 Continuity
2 Properties of continuous functions
3 The intermediate value theorem
4 Bounds of continuous functions
5 A continuous function in a closed interval attains its bounds
6 Uniform continuity
7 Uniform continuity theorem
8 Inverse functions
9 Existence theorem for an inverse function
10 Maxima and minima
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