Which of the following possible values of k is NOT consistent if y = f (x) is continuous, monotonic, and concave down for all values of x? 0.5, -2, 0, 1, or 6?

Question

anonymous · Answer

I am having issues understanding the wording on some the question on my review, and I just don't get the question.

anonymous · Answer

Are you sure that is all of the question? They didn't say anything about k?

anonymous · Answer

I know! That is why I am so confused. :/ Wouldn't the answer hinge on what /kind/ of function this was, and why role k played in said function? This is all that's listed in the question though so I wasn't sure what to do...

anonymous · Answer

I'm thinking about just saying -2 because it is the only negative value listed and I imagine that it would affect the concavity of whatever function this is, especially since all the other values are positive. Do you think that's what I should answer?

jim_thompson5910 · Answer

My guess is that f(x) = k*g(x) for some other function g(x)


Since f is monotonic over the entire domain, then f is either always increasing or decreasing over the entire domain.


But if k = 0, then f(x) = 0 for all x over the domain...which wouldn't make it monotonic at all.

jim_thompson5910 · Answer

So k = 0 is your answer

anonymous · Answer

So basically (if we assume that the function you're using is what they meant), if k=0 it would just be a line, neither decreasing or increasing?

jim_thompson5910 · Answer

It'd be a horizontal line y = 0, which is basically the x-axis, which is neither increasing nor decreasing. So it's not a monotonic function.

anonymous · Answer

I suppose that would also make it neither concave up nor down, so that must be the answer. Thank you!

jim_thompson5910 · Answer

Of course, this is all hinged on the assumption that we're talking about something like f(x) = k*g(x)

jim_thompson5910 · Answer

Yes if k = 0, then it's second derivative is also zero, meaning that it's neither concave up or down.

anonymous · Answer

Thanks, if by chance that isnt the function, I think I have a good argument since the question was so vague.

jim_thompson5910 · Answer

Good point, that's what I'd go with too (unless they're referencing some other part/problem in your book).