- #1

NoahsArk

Gold Member

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## Summary:

- Help Understanding the Importance of Second Derivatives

## Main Question or Discussion Point

Hello. My understanding of the importance of second derivatives is that they help us to know whether the graph of a function is concave upward or concave downward. In the equation ## f(x) = x^2 + 2x ## we already know from the first derivative, ## f\prime (x) = 2x + 2 ##, that the graph is concave upward because the 2 in front of the x is positive. Why do we need to even figure out the second derivative, which is also a positive number, 2, to determine that? Seems like we are taking an unnecessary step. Thanks.