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An inflection point where the second derivative doesnt exist? A point of inflection exists where the concavity changes Where the derivative is increasing the graph is concave up; where the derivative is decreasing the graph is concave down Concavity may change where the second derivative is 0 or undefined You said that the graph must be continuous I'm not sure that's true, but if it is then this still works The graph can be continuous even if the
Difference between undefined and does not exist What is the difference between the terms "undefined" and "does not exist", especially in the context of differential calculus? Most calculus materials state, for example, that $\frac {d} {dx} {|x|}
Which is correct: negative infinity or does not exist? I don't think DNE is unambiguously wrong, as there's no standard definition for what it means In many calculus classes, a limit is said not to exist if there is no real limit, and positive negative infinite limits are a subset of these
Showing limit does not exist using two-path test I am new to using two-path test and my textbook only discusses it without showing any examples I attempted to do this question below but I am not sure if I am correct The question says to show the
How to find the critical numbers of a trig function When you say "critical numbers" do you, perhaps, means either critical points or critical values? Critical points are the $\theta$ for which $\mathrm {g}' (\theta)=0$ while critical values are the values that $\mathrm {g}$ takes at critical points, i e $\mathrm {g} (\theta)$