Question

A method for determining whether a critical point is a minimum

Answer 1

Answer:

First and Second Derivative Tests. First identifies critical points. The second determines behavior around the point.

• Concave up is a minimum
• Concave down is a maximum

Step-by-step explanation:

The extreme points of a function are called the maximum and/or minimums. AT these points, the function (or y-values) are at their highest or lowest. These points are often the peaks and valleys of a function on a graph. You can determine if a function has max or min using the first and second derivative tests. The first determines critical points of the function. The second determines behavior around a point. If the value is positive then the function is concave up. It forms a valley and the point is a minimum. If the value is negative then the function is concave down. It forms a peak which has a maximum.