I asked a question to the two AP calculus teachers today, and I think we’ve concluded that we each aren’t 100% sure of the answer. It’s one of those questions that seems so basic that how could we not be sure?
I’m going to put up two graphs (of the square root of x). Can you tell me what intervals the following function are increasing on? [Notice the difference: Function A is defined at x=0, Function B is not defined at x=0.]
According to Anton’s Calculus text, it says:
Let be a function that is continuous on a closed interval and differentiable on the open interval .
If for every value of in , then is increasing on .
If for every value of in , then is decreasing on .
According to Rogawski’s Calculus text, it says:
Let be a differentiable function on the open interval .
If for , then is increasing on
If for , then is decreasing on
So my questions are: Are these two different definitions? I’m not teaching AP Calculus, but would this even be an issue for the AP exam? And why am I so not getting this?