Which Interval Shows f' Always Increasing?

[karush]

View attachment 9411image due to macros in overleaf

well apparently all we can do is solve this by observation
which would be the slope as x moves in the positive direction
e appears to be the only interval where the slope is always increasing

 

[tkhunny]

image due to macros in overleaf

well apparently all we can do is solve this by observation
which would be the slope as x moves in the positive direction
e appears to be the only interval where the slope is always increasing

You have not correctly understood or interpreted the question. e is a point, not an interval.

"always increase" doesn't mean anything for a point. Either it's increasing at that point or it isn't.

 

[karush]

Ok good point

Well at point e the slope is increasing

 

[HallsofIvy]

At point a the function is decreasing so f' is negative, not positive. At point b there is a cusp so f' does not even exist there. At point c the function is increasing so f' is positive but the graph is "flattening" so f' is decreasing, not increasing. At point d the function is decreasing so f' is negative, not positive. At point e the function is increasing so f' is positive and the graph is getting steeper so f' is increasing. Yes, e is the correct answer.