graph and derivatives

[Dorian Gray]

Greetings Math friends,
I am having issues with the problem in the picture. Unfortunately, I have never seen a problem like this before and do not know how to address it. Any comments, help, or suggestion about tackling this problem would be much appreciated. Thank you

 

[Deleted member 4993]

Greetings Math friends,
I am having issues with the problem in the picture. Unfortunately, I have never seen a problem like this before and do not know how to address it. Any comments, help, or suggestion about tackling this problem would be much appreciated. Thank you



View attachment 1677

First decide which of those parameters are >0 and which are <0.

 

[Dorian Gray]

Thank you for your response Subhotosh Khan. However, I am not exactly sure what you mean by parameters (I am in calculus one and have only had it for a couple of weeks and this is a brand new chapter. We have only covered chapter one , which was strictly over limits. This new chapter is about derivatives), and how they will help determine the values of each of those points...

 

[pka]

Thank you for your response Subhotosh Khan. However, I am not exactly sure what you mean by parameters (I am in calculus one and have only had it for a couple of weeks and this is a brand new chapter. We have only covered chapter one , which was strictly over limits. This new chapter is about derivatives), and how they will help determine the values of each of those points...

The \(\displaystyle g'(a)\) is the slope of the tangent to the graph at \(\displaystyle (a,g(a))\).
Picture that line at values. Arrange the slopes in increasing order.

 

[Dorian Gray]

Thanks!

Ohhhhhh I see what the problem is looking for now. Thank you very much. What would be the difference then between the 0 and the g'(0)? Would they be the same?

 

[Dorian Gray]

clarification

Thank you for the clarification JeffM. I understand the difference of the values for 0 and g'(0).

I would say that the order would then be this:

g'(0) because the slope is something negative

0 because it is a point and is not negative or positive

g'(4) because it is a positive slope but less than the others with positive slopes

g'(2) because it has the second steepest positive slope

and the highest would then be g'(-2) because that has the steepest positive slope.