Video 3.4.1. Concavity and the 2nd Derivative Test.
The concavity of a function can be determined using the second derivative test. If the second derivative is positive at a critical point, the function is concave up and the critical point is a relative minimum. If the second derivative is negative, the function is concave down and the critical point is a relative maximum.We have previously seen how the first derivative told us intervals where a function was increasing and decreasing. Now we look to what the second derivative can tell us, a property we refer to as concavity.
Post-video reflection.
Both the 1st and 2nd derivative provide us information about whether a critical point is a max or min. Which method do you prefer? Do you always prefer it, or does it depend?
