Differential analysis: convex functions

[madafo3435]

TL;DR

I am reading A Course in Mathematical Analysis Volume 1 by D. J. H. Garling, and I am having trouble in the following demonstration of Section 2 Differentiation. part 4 of the test, the first part of the second inequality does not make sense, I do not understand its justification. I hoped they can help you understand the inequality, or how to do the test correctly, as this seems like a Garling mistake.

I am reading A Course in Mathematical Analysis Volume 1 by D. J. H. Garling, and I am having trouble in the following demonstration of Section 2 Differentiation. part 4 of the test, the first part of the second inequality does not make sense, I do not understand its justification. I hoped they can help you understand the inequality, or how to do the test correctly, as this seems like a Garling mistake.

 

[Office_Shredder]

By the first part of the second inequality, do you mean the f'(a+) <f'(b-)? If not can you be a bit more specific about which part you don't understand?

 

[madafo3435]

By the first part of the second inequality, do you mean the f'(a+) <f'(b-)? If not can you be a bit more specific about which part you don't understand?

I have already solved it, thanks anyway