Increasing/Decreasing & Max/Min & Zeros/Factors

Front

What does it mean for a function to be increasing?

Back

A function is increasing on an interval if, as the input values (x) increase, the output values (y) also increase.

Front

What does it mean for a function to be decreasing?

Back

A function is decreasing on an interval if, as the input values (x) increase, the output values (y) decrease.

Front

Define local maximum.

Back

A local maximum is a point on the graph of a function where the function value is higher than the values of the function at nearby points.

Front

Define local minimum.

Back

A local minimum is a point on the graph of a function where the function value is lower than the values of the function at nearby points.

Front

What are zeros of a function?

Back

Zeros of a function are the values of x for which the function f(x) = 0.

Front

What is a factor of a polynomial?

Back

A factor of a polynomial is a polynomial that divides the original polynomial without leaving a remainder.

Front

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

Back

To find intervals of increase or decrease, analyze the first derivative of the function. If f'(x) > 0, the function is increasing; if f'(x) < 0, it is decreasing.

Front

What is the significance of the first derivative test?

Back

The first derivative test helps determine whether a critical point is a local maximum, local minimum, or neither.

Front

What is the range of a function?

Back

The range of a function is the set of all possible output values (y) that the function can produce.

Front

What does it mean for a function to be constant over an interval?

Back

A function is constant over an interval if it takes the same value for all x in that interval.