(Part 1) M4 Review for FINALS (Fall 2024)

Front

What is a piecewise function?

Back

A piecewise function is a function that is defined by different expressions or formulas for different parts of its domain.

Front

How do you evaluate a piecewise function?

Back

To evaluate a piecewise function, identify the interval in which the input value falls and use the corresponding expression to find the output.

Front

What is an absolute maximum value of a function?

Back

The absolute maximum value of a function on a given interval is the highest value that the function attains within that interval.

Front

How do you determine local minimum values of a function?

Back

Local minimum values occur at points where the function changes from decreasing to increasing, typically found using the first derivative test.

Front

What does it mean for a function to be increasing on an interval?

Back

A function is increasing on an interval if, for any two points in that interval, the function's value at the second point is greater than at the first.

Front

What is the significance of critical points in a function?

Back

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

Front

How do you find the intervals of increase and decrease for a function?

Back

To find intervals of increase and decrease, analyze the sign of the derivative: positive indicates increasing, negative indicates decreasing.

Front

What is the difference between local and absolute extrema?

Back

Local extrema are the highest or lowest points in a small neighborhood, while absolute extrema are the highest or lowest points over the entire domain.

Front

What is the role of the first derivative in analyzing functions?

Back

The first derivative indicates the slope of the function; it helps determine increasing/decreasing behavior and locate critical points.

Front

How do you find the value of a function at a specific point using a piecewise function?

Back

Substitute the specific point into the appropriate piece of the piecewise function based on its defined intervals.