State the range of values of f '(x)

[Workedmisty]

I was looking through a past paper and couldn't understand this question

I was able to do each part, up until part c. I've looked at the answers () and cannot understand how this was reached

 

[tkhunny]

What did part (a) look like?

 

[Dr.Peterson]

You have to trust the picture, specifically that the part of the graph shown is concave upward; that is, the derivative is increasing for negative x. Therefore, what is the greatest value of f'(x)? What is the smallest value of f'(x)?

You'll want to do the same with the rest of the graph as you made it for part (a). This will not change your answers as found in the given part of the graph; think about what that is.

 

[Workedmisty]

What did part (a) look like?

 

[Dr.Peterson]

Good. Now where is the curve steepest? Where is it least steep?

 

[Workedmisty]

Good. Now where is the curve steepest? Where is it least steep?

Oh I get it now! Thank you so much.

Least steep at the asymptotes, so lower value of 1/2 and most steep at 0, so higher value at 2.