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5.7 Using the Second Derivative Test to Determine Extrema
1 min read•june 8, 2020
Sumi Vora
🎥Watch: AP Calculus AB/BC - Concavity and f, f', f''
Resources:
Concavity
@sander-o
•Nov 11, 2020
f, f', f''
@jenni513843
•Nov 11, 2020
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. ❗️
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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. 🙋♂️
Example Problems
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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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