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

But how?
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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