This Monotonicity problem accepts an answer that doesn’t seem correct to me. I’m wondering if anyone encountered this?
Thanks! – Andrew
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I believe the webwork is right. The red answer is incorrect because in the domain (-inf,0)U(0,0.5952) is saying that 0 is not include in the domain and the green (-inf,.5952) is correct because it is saying 0 is include in the domain. The answer accept the green because the webwork want 0 to be include in the domain.
At 0 the tangent line is horizontal. Is it still considered to be decreasing?
Hi guys. Good catch Andrew! Usually, we’d say that f(x) is decreasing at x=c if f'(x)<0. Since your f'(0)=0, then f(x) is neither increasing nor decreasing at x=0. This isn't the most important distinction in the world…you might imagine that we'd instead say that f(x) is decreasing at x=c if f'(x) is less than or equal to 0, and then f(x) is STRICTLY decreasing at x=c if f'(x)<0. It is important to know which convention is being used though.
I'm in the first camp: I prefer to say that f(x) is decreasing at x=c if f'(c)<0. Let me know if there's another place where WebWork is using the other convention.
Looked and found an example of Webwork wanting the opposite of what it wants in the problem posted above:
CurveSketching Asymptotes: Problem 2 Accepts only a union of intervals when the curve is flat at one point. So there is an inconsistency. It wasn’t a problem as it reinforced my understanding of what’s happening to have to figure out what Webwork wanted.
Oops, wish I could undo posts. Scratch the above. CurveSketching Asymptotes: Problem 2 has an infinite discontinuity at the point. I’ll keep looking.
I didn’t turn up any inconsistency after all. Webwork problems from the four sets appear to treat increasing and decreasing the same way in all cases.