Adam W. answered • 02/05/20
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Finance/Economics/Math/Stats Tutoring from an Algorithmic Trader
In Differential Calculus, the point of inflection is a point where the concavity changes.
A necessary condition for x to be a point of inflection is f''(x)=0, and a sufficient condition is that sgn(f''(x+e)) = - sgn(f''(x-e)) for some small e>0. In other words, the curvature (second derivative) changes signs around some small neighborhood of x.
Once you solve for f''(x), check these two conditions.
Adam W.
Were you able to solve for the second derivative f''(x)? This can be done "term-by-term", i.e. f''(x) = d/dx (xsinx) + d/dx (-coshx). From there, take the 4 possible answers and check which ones satisfy: i) f''(x)=0 ii) If the sign of f''(x-e) and f''(x+e) are opposite.
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02/05/20
Allison D.
thank you, I still don't know how to do those other steps and I know this question will be on my upcoming ap calc test.02/05/20