- 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.