Help me understand this textbook example (Calculus Limits & Derivatives).

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Help me understand this textbook example (Calculus Limits & Derivatives).

Mathematics
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I don't understand how slope is 3/2.
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Oh, i think they are just supposing that the "slope" at x=5 turned out to be 3/2.
They are trying to introduce the notation. Tell me, you might have heard that the "derivative" is the "slope", have you?

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yes. here is the next part
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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?
In the example from the pictures, I don't know how they gotten the slope as 3/2. So, I want to know how they got it.
They are telling you this (for part 1): Suppose the slope of the function f, at x=5 is approximately equal to 3/2. You know that the slope/derivative at every x on the function is denoted by f`(x), and thus the slope of the function at at a particular value of x=c is denoted by f'(c). So, to denote that \(\large"\)the slope/derivative of the function at x=5 is approximately 3/2 \(\large"\), --> you will write: f`(5) ≈ 3/2
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.
Yeah, they have a graph for ` f(x) `. That is the graph of the function in \(\LARGE \color{blue}{\rm _{^{blue}}}\), it is the first graph. You will agree that a particular point at ` x=c ` will be ` ( c,f(c) ) `. Then, you got a \(\LARGE \color{purple}{\rm _{^{purple}}}\) graph, it is the second graph and it is for the derivative (or the slope) of the function f(x), and it is denoted by: ` f '(x) `. ---> The slope at x=c will be given by f'(c). So the (c,f(c)) gives you the point at x=c, and f'(c) gives you the instantaneous slope of that point.
Observe the point B on the graph of f(x). You will see that the B' (the derivative of B), is B'=0.

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