1 min readβ’june 8, 2020

Sumi Vora

If we combine our knowledge of first derivatives and second derivatives, we find that we can use the **second derivative** to **determine whether a critical point is a relative minimum or relative maximum**.Β βοΈ

In other words, if we know that there is a local extreme at a certain point and the graph is **concave up at that point, it must be a minimum**, and, if the graph is **concave down at that point, it must be a maximum**. πββοΈ

We can find the critical points of implicit functions in a similar manner. The critical points occur when **dy/dx = 0**.

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