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Oh, i think they are just supposing that the "slope" at x=5 turned out to be 3/2.

Yes, and what about it?

I still don't see how they got 3/2 as the slope

Did you mean the definition of a derivative?

what exactly are you trying to ask me?

Ok, thanks.

And for part 2, what exactly do you want to know?

Posted there in-case more information was needed as that is the expanded part of the example.

Observe the point B on the graph of f(x). You will see that the B' (the derivative of B), is B'=0.