Question

can someone explain the 2nd derivative test?

Answer 1

is for determining whether a given stationary point of a function is a local maximum or a local minimum using the value of the second derivative at the point.

Answer 2

The function can attain a max or min only at a point where the first derivative is zero. If the second derivative is negative at that point (value of x) the function attains a maximum. If the second derivative is positive at that point, the function attains a minimum. If the second derivative is zero, the test is inconclusive.

Answer 3

can you give an example of how to do it?

Answer 4

From a Calc 1 standpoint:

The second derivative test is meant to figure out the highest point on your first derivative. In short, where the second derivative is zero, your first derivative is either at a Max or a Min. And remember, your derivative is just the instantaneous rate of change, meaning where the Second derivative is zero, your original function is undergoing the steepest change or the flattest change. In short, you use the second derivative test to find inflection points and to determine concavity.

Answer 5

How to do it: take the first derivative, find the roots. Find the second derivative, and evaluate it at the roots of the first derivative. If the second derivative is positive or negative you have identified a place where the function attains a min/max.