Question

How to find local maxima and minima?

A. Set the derivative equal to zero and solve for x.
B. Set the equation equal to zero and solve for x.
C. Take the limit as x approaches infinity.
D. Find the critical points and evaluate the function at those points.

Answer 1

To determine local maxima and minima, one should find the derivative of a function, set it to zero to get critical points, and use the second derivative test to identify the nature of those points.

Step-by-step explanation:

To find local maxima and minima, one must:

1. Take the derivative of the function and set it equal to zero to solve for x. This step finds the critical points.
2. Use the second derivative test to determine whether each critical point is a maximum or minimum. If the second derivative at a critical point is positive, the function has a local minimum there; if it is negative, the function has a local maximum.

This method reflects option D from the choices given. The critical points are where the first derivative equals zero or does not exist. After finding the critical points, the second derivative can confirm if those points are maxima or minima.

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