Key Features of Functions

Front

What is a maximum point of a function?

Back

A maximum point of a function is a point where the function value is greater than or equal to the values of the function at nearby points.

Front

What is a minimum point of a function?

Back

A minimum point of a function is a point where the function value is less than or equal to the values of the function at nearby points.

Front

How do you identify intervals where a function is positive?

Back

A function is positive on an interval if all the function values are greater than zero for all x in that interval.

Front

How do you identify intervals where a function is negative?

Back

A function is negative on an interval if all the function values are less than zero for all x in that interval.

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 x1 and x2 in that interval, if x1 < x2, then f(x1) < f(x2).

Front

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

Back

A function is decreasing on an interval if, for any two points x1 and x2 in that interval, if x1 < x2, then f(x1) > f(x2).

Front

What is end behavior of a function?

Back

End behavior describes how the values of a function behave as x 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, indicating potential maximums, minimums, or points of inflection.

Front

How do you find the maximum and minimum points of a function?

Back

To find maximum and minimum points, calculate the derivative, set it to zero to find critical points, and use the second derivative test or analyze the sign changes.

Front

What is the first derivative test?

Back

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