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# 5.7 Using the Second Derivative Test to Determine Extrema

Sumi Vora

### AP Calculus AB/BCΒ βΎοΈ

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π₯Watch: AP Calculus AB/BC - Concavity and f, f', f''

## Using the Second Derivative Test

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 βοΈ
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. πββοΈ

## Example Problems

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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