Math 3 Extrema Flashcard

Front

What is an absolute maximum in a function?

Back

The absolute maximum of a function is the highest point over the entire domain of the function. It is the largest value that the function attains.

Front

How do you determine where a function is increasing or decreasing?

Back

A function is increasing on an interval if the derivative is positive on that interval, and it is decreasing if the derivative is negative.

Front

What is a relative maximum?

Back

A relative maximum is a point in the domain of a function where the function value is higher than the values of the function at nearby points.

Front

What does end behavior of a function refer to?

Back

End behavior describes how the values of a function behave as the input approaches positive or negative infinity.

Front

What is the significance of critical points in a function?

Back

Critical points are where the derivative is zero or undefined, and they are potential locations for relative maxima, minima, or points of inflection.

Front

How can you identify intervals of increase and decrease from a graph?

Back

By observing the slope of the tangent line: if the slope is positive, the function is increasing; if negative, it is decreasing.

Front

What is the first derivative test?

Back

The first derivative test is a method used to determine whether a critical point is a relative maximum, minimum, or neither by analyzing the sign of the derivative before and after the point.

Front

What is the difference between absolute and relative extrema?

Back

Absolute extrema are the highest or lowest points over the entire domain, while relative extrema are the highest or lowest points in a specific interval.

Front

What does it mean for a function to have ↑ & ↓ end behavior?

Back

It means that as x approaches positive or negative infinity, the function's values increase or decrease, respectively.

Front

How do you find the intervals where a function is decreasing?

Back

Identify where the derivative of the function is negative; these intervals indicate where the function is decreasing.