Question

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

Answer 1

I don't understand how slope is 3/2.

Answer 2

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

Answer 3

They are trying to introduce the notation.
Tell me, you might have heard that the "derivative" is the "slope", have you?

Answer 4

yes. here is the next part

Answer 5

Yes, and what about it?

Answer 6

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

Answer 7

Did you mean the definition of a derivative?

Answer 8

what exactly are you trying to ask me?

Answer 9

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.

Answer 10

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

Answer 11

Ok, thanks.

Answer 12

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

Answer 13

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

Answer 14

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.

Answer 15

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