Question

Classify the critical points as local maxima, local minima or neither. briefly explain.

Option 1: Local maximum
Option 2: Local minimum
Option 3: Neither
Option 4: Need more information

Answer 1

To classify critical points as local maxima, local minima, or neither, we can use the second derivative test.

Step-by-step explanation:

To determine if a critical point is a local maximum, local minimum, or neither, we can use the second derivative test. If the second derivative is positive at a critical point, then it is a local minimum. If the second derivative is negative, then it is a local maximum. If the second derivative is zero or does not exist, the test is inconclusive.

For example, let's say we have a function f(x) and we find that f'(a) = 0. We can then find the second derivative f''(a). If f''(a) > 0, then the critical point a is a local minimum. If f''(a) < 0, then it is a local maximum. If f''(a) = 0 or f''(a) does not exist, the classification is inconclusive.