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

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Zenmo
 one year ago
Best ResponseYou've already chosen the best response.0I don't understand how slope is 3/2.

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1Oh, i think they are just supposing that the "slope" at x=5 turned out to be 3/2.

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1They are trying to introduce the notation. Tell me, you might have heard that the "derivative" is the "slope", have you?

Zenmo
 one year ago
Best ResponseYou've already chosen the best response.0yes. here is the next part

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1Yes, and what about it?

Zenmo
 one year ago
Best ResponseYou've already chosen the best response.0I still don't see how they got 3/2 as the slope

Zenmo
 one year ago
Best ResponseYou've already chosen the best response.0Did you mean the definition of a derivative?

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1what exactly are you trying to ask me?

Zenmo
 one year ago
Best ResponseYou've already chosen the best response.0In 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.

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1They 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

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1And for part 2, what exactly do you want to know?

Zenmo
 one year ago
Best ResponseYou've already chosen the best response.0Posted there incase more information was needed as that is the expanded part of the example.

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1Yeah, 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.

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1Observe 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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