Question

How to find the relative maxima and minima of a function.

A) Critical points of the derivative
B) Points of inflection
C) Points of intersection with the y-axis
D) Local maxima and minima

Answer 1

To find the relative maxima and minima of a function, you can follow these steps: find the critical points of the derivative, determine the points of inflection, check the points of intersection with the y-axis, and analyze the behavior of the function around the critical points to identify local maxima and minima.

Step-by-step explanation:

To find the relative maxima and minima of a function, you can follow these steps:

1. Find the critical points of the derivative of the function. These are the points where the derivative is equal to zero or does not exist.
2. Determine the points of inflection, which are the points where the concavity of the function changes. These can be found by finding the x-values where the second derivative of the function is equal to zero or does not exist.
3. Check the points of intersection with the y-axis by plugging in x=0 into the original function and identifying the corresponding y-values.
4. Finally, analyze the behavior of the function around the critical points to determine if they are local maxima or minima. You can do this by evaluating the sign of the derivative in intervals around the critical points.