# Thread: Function points monotonic and increasing help?

1. ## Function points monotonic and increasing help?

Can anyone take a look at this question: and tell me if my answer is correct? If not why not? I've already gotten some help with derivatives and second derivatives and how they behave compared to the original function, but I'm not sure about the "monotonic" meaning, I'm also not sure if the brackets change the outcome of option III. Any help? Thanks!

2. ## Re: Function points monotonic and increasing help?

Monotonic means if it increases, it does not also decrease. If it decreases, it does not also increase. Since it increases, it can be monotonic if and only if it does not decrease (which is true). The derivative can be approximated by taking the slope of the lines between adjacent points. Those slopes would be 1,2,3. So, it is possible that f'(x) is increasing. Next, II and III are saying the exact same thing. If II is true, then so is III (and vise versa). For III, you can only discount something if you have evidence to the contrary. Since you do not know if the function exists for x<-0.5 or x>-0.2, you cannot discount that it is possible. There is no evidence to the contrary, so it is possible.

3. ## Re: Function points monotonic and increasing help?

Originally Posted by SlipEternal
Monotonic means if it increases, it does not also decrease. If it decreases, it does not also increase. Since it increases, it can be monotonic if and only if it does not decrease (which is true). The derivative can be approximated by taking the slope of the lines between adjacent points. Those slopes would be 1,2,3. So, it is possible that f'(x) is increasing. Next, II and III are saying the exact same thing. If II is true, then so is III (and vise versa). For III, you can only discount something if you have evidence to the contrary. Since you do not know if the function exists for x<-0.5 or x>-0.2, you cannot discount that it is possible. There is no evidence to the contrary, so it is possible.
Okay, thank you. Would III just be decreasing though? Is it possible to know if it's concave up or just decreasing?

4. ## Re: Function points monotonic and increasing help?

Concave up means the derivative is increasing. Concave down means the derivative is decreasing.

5. ## Re: Function points monotonic and increasing help?

Originally Posted by SlipEternal
Concave up means the derivative is increasing. Concave down means the derivative is decreasing.
So aren't they all true then?

6. ## Re: Function points monotonic and increasing help?

Yes, that's what SlipEternal said.

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