Question

Find all the local maxima, local minima, and saddle points of the function

Answer 1

To find local maxima, minima, and saddle points, find critical points using the first derivative test and then apply the second derivative test.

Step-by-step explanation:

To find the local maxima, local minima, and saddle points of a function, we first need to find the critical points. These are the points where the derivative of the function is either zero or undefined. To check whether each critical point is a local maxima, local minima, or saddle point, we use the second derivative test.

The second derivative test states that if the second derivative is positive at a critical point, then the point is a local minimum. If the second derivative is negative, then the point is a local maxima. If the second derivative is zero, the test is inconclusive.

By applying the second derivative test to each critical point, we can determine whether it is a local maxima, local minima, or saddle point.

Answer 2

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