Question

How to find the min and max of a function?

A) The min and max occur at the points where the function intersects the x-axis.
B) The min and max occur at the points where the derivative is zero or undefined.
C) The min and max occur at the points where the function is concave up.
D) The min and max occur at the endpoints of the domain.

Answer 1

To find the min and max of a function, we look for points where the derivative is zero or undefined. This is called critical points. The min and max can also occur where the function is concave up.

Step-by-step explanation:

To find the min and max of a function, we look for points where the derivative is zero or undefined. This is option B. At these points, the slope of the function is either flat (derivative is zero) or undefined (vertical tangent line). These points are called critical points. We can also check the endpoints of the domain to see if they are the min or max. It's important to note that the min and max can also occur where the function is concave up, which is not mentioned in the options.