Hi my textbook uses the second derivative method to find inflection points. Now since inflection points are when the concavity changes direction, and if the graph of f is concave upward if f' is increasing on that interval and vice versa, isn't it possible to just use the first derivative to find points of inflection?
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No - how so would you use the first derivative?
You would test if each interval was concave up or down using the 1st derivative
say I have function y=x^3-5x^2+x-10
How would you test for concave up and concave down?
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Find crit values by making the derivative = 0, and then test each interval between that applies. If the derivative is increasing, then the original function is concave up, and if the derivative is decreasing, then it must be concave down. Whenever it changes from concave up to concave down or vice versa, it must be an inflection point.
if the derivative is increasing?
that means the second derivative is positive. You see, if the derivative is increasing, that means you are thinking about the second derivative @Sujay
and why don't we just take a derivative from two points and see if there is a decrease or increase in those two points? well the reason is because there's no way to tell what happens in between...
@Sujay , do you follow?
Alright thanks, I believe I see what you guys are saying now.