Should I press my Mother to get tested for memory issues?

You helped me before with questions about caring for my 88 year old mother. She lives alone, but is still fairly active physically (two walks a day!) and socially in her gated community. Still. She has become increasingly forgetful these past few years. Books she has read, physical issues she's had, experiences, dates seem to be missing from her memory bank. Recently, she's had a lot of problems with remembering appointments - a walking date she's set up, for example, with a friend for the following day, an appointment with her dentist - wrong day, wrong time. And a book she read two months ago, she's just picked up to read it again, saying it's been along time since she'd read this book. These seem like small things. Are they? My grandmother, her mother, had Alzheimer's. I understand it can run in the family. If my mother just having normal aging memory issues that's one thing. If it's Alzheimer's though, is this something that we should know now? And if so, how on earth can I get my mother, my very proud, uncomplaining, strong-willed mother to go in and get tested? Best to let this all go and just wait it out for a crisis? Maybe all I need to hear is that there is nothing to be done, that I don't have to do anything about this. Anyway, your thoughts would be appreciated.

Thank you,
Beth