'John Clements' via Racket Users cites Jens Axel Søgaard:
The root finder is the right tool.
Excellent. That makes a lot of sense. Given the setup, I think  h = 0.0001 is 
probably plenty small. It didn’t occur to me that I could differentiate 
numerically, rather than analytically. Thanks!
If your function is defined segment-wise, using numerical differentiantion might be dangerous, the program may take silly decisions. *In general* minimizing a function by looking for zeros of the derivative is considered inefficient and not really stable. The root finder is not the right tool. You may use this derivative - if you wish - for the gradient descent procedure.

Jerzy Karczmarczuk

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