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I am reading "Introduction to Real Analysis" (Fourth Edition) by Robert G Bartle and Donald R Sherbert ...
I am focused on Chapter 6: Differentiation ...
I need help in fully understanding the corollary to Theorem 6.2.1 ...Theorem 6.2.1 and its corollary ... ... read as follows:
View attachment 7295
Can someone please demonstrate how to prove Corollary 6.2.2 above ...Note that ... obviously ... if the derivative of $$f$$ exists then since $$c$$ is an interior point at which $$f$$ has a relative extremum then $$f'(c) = 0$$ by Theorem 6.2.1 ... maybe this forms part of the proof ...
Hope someone can help ...
Peter
I am focused on Chapter 6: Differentiation ...
I need help in fully understanding the corollary to Theorem 6.2.1 ...Theorem 6.2.1 and its corollary ... ... read as follows:
View attachment 7295
Can someone please demonstrate how to prove Corollary 6.2.2 above ...Note that ... obviously ... if the derivative of $$f$$ exists then since $$c$$ is an interior point at which $$f$$ has a relative extremum then $$f'(c) = 0$$ by Theorem 6.2.1 ... maybe this forms part of the proof ...
Hope someone can help ...
Peter