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. ❗️
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. 🙋♂️
We can find the critical points of implicit functions in a similar manner. The critical points occur when dy/dx = 0.
Thousands of students are studying with us for the AP Calculus AB/BC exam.join now
Browse Study Guides By Unit
5.7Using the Second Derivative Test to Determine Extrema