How can I calculate the derivative of this function?

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Homework Help Overview

The discussion revolves around calculating the derivative of a function f(x) at specific points a = 1, 2, 4, and 7, based on a graph that is referenced but not provided. Participants are exploring the concept of derivatives and their geometric interpretations.

Discussion Character

  • Exploratory, Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants discuss the geometric interpretation of the derivative, questioning what f'(a) represents in relation to the graph. There are attempts to relate the definition of the derivative to the problem at hand, and some participants suggest using visual inspection of the graph to determine slopes.

Discussion Status

The discussion is active, with participants sharing insights about the geometric meaning of derivatives and exploring how to apply this understanding to the specific points of interest. There is a mix of interpretations and approaches being considered, with no explicit consensus reached yet.

Contextual Notes

Participants note the absence of the graph, which is crucial for determining the slopes at the specified points. The original poster's request for help indicates a need for guidance in understanding how to approach the problem without complete information.

GaussianSurface

Homework Statement


Let f(x) be the function whose graph is shown below (I'll upload the image)

Determine f'(a) for a = 1,2,4,7.

f'(1) =

f'(2) =

f'(4) =

f'(7) =

Use one decimal.

Homework Equations


f(x+h)-f(x)/h

The Attempt at a Solution


Hi everybody I was trying to do this function but I haven't been able to do it even though I'm supposing some things about how this problem can be compute, so I want to ask for help so some of you can guide me to the final result, hope some of you all can help me.
 

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When consdering some function ##f(x)##, what is a geometric interpretation of ##f'(a)##?
 
MarkFL said:
When consdering some function ##f(x)##, what is a geometric interpretation of ##f'(a)##?

I guess it's not specified, actually I had the same problem I was wondering what's ƒ'(a) since it is not in the graph they gave me...
 
What I mean is, in your study of the derivative, what have you been taught that the derivative can represent geometrically, that is, in relation to the graph of the function?
 
MarkFL said:
What I mean is, in your study of the derivative, what have you been taught that the derivative can represent geometrically, that is, in relation to the graph of the function?
Well, it can represent the slope or the instantaneuos rate of change. that's how they've taught me, is that what you wanted to know?
 
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GaussianSurface said:
Well, it can represent the slope or the instantaneuos rate of change. that's how they've taught me, is that what you wanted to know?

Yes, that's what I was after. :biggrin:

So, can you determine the instantaneous slope of the given function's graph at the given values of ##a##?
 
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MarkFL said:
Yes, that's what I was after. :biggrin:

So, can you determine the instantaneous slope of the given function's graph at the given values of ##a##?

Let me see if I got you.

Since you asked about to determine the insatataneous slope I'd say that we can do it by the defnition of derivative ( the one that I posted above ) so far am I going in the good way?
 
GaussianSurface said:
Let me see if I got you.

Since you asked about to determine the insatataneous slope I'd say that we can do it by the defnition of derivative ( the one that I posted above ) so far am I going in the good way?

It's actually more simple than that...you can "eyeball" the slope of the function at the given points...:wink:
 
MarkFL said:
It's actually more simple than that...you can "eyeball" the slope of the function at the given points...:wink:
Mmmm... Shall I take the prime points at x and compare with f'(a) and so on...?
 
  • #10
Place a dot on your curve above each of the x-values where you are asked to find a value for f’

This will highlight exactly which points on the plot are under discussion.
 
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  • #11
GaussianSurface said:
Mmmm... Shall I take the prime points at x and compare with f'(a) and so on...?

First, let's consider the function where ##0<x<3##...we have a horizontal line...what is the slope of a horizontal line?
 
  • #12
NascentOxygen said:
Place a dot on your curve above each of the x-values where you are asked to find a value for f’

This will highlight exactly which points on the plot are under discussion.
Ohh! I think got it when the prime values get x then a value f'(x) changes with it, doesn't it?
 
  • #13
GaussianSurface said:
Ohh! I think got it when the prime values get x then a value f'(x) changes with it, doesn't it?
I can't decide whether you can see the answers or not. As MarkFL indicated, the values of f' in this exercise can be decided by mere inspection. Remember, f'(b) is the slope of the curve f around point b.
 

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