## Zenmo one year ago Help me understand this textbook example (Calculus Limits & Derivatives).

1. Zenmo

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

2. SolomonZelman

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

3. SolomonZelman

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

4. Zenmo

yes. here is the next part

5. SolomonZelman

6. Zenmo

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

7. Zenmo

Did you mean the definition of a derivative?

8. SolomonZelman

what exactly are you trying to ask me?

9. Zenmo

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.

10. SolomonZelman

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

11. Zenmo

Ok, thanks.

12. SolomonZelman

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

13. Zenmo

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

14. SolomonZelman

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.

15. SolomonZelman

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