1.2 Increasing/Decreasing Intervals

Front

What are increasing intervals in a function?

Back

Increasing intervals are ranges of x-values where the function's output (y-value) is rising as x increases.

Front

What are decreasing intervals in a function?

Back

Decreasing intervals are ranges of x-values where the function's output (y-value) is falling as x increases.

Front

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

Back

To determine where a function is increasing or decreasing, analyze the first derivative of the function. If the derivative is positive, the function is increasing; if negative, it is decreasing.

Front

What does it mean if a function has a local maximum?

Back

A local maximum is a point where the function value is higher than all nearby points, indicating a peak in the graph.

Front

What does it mean if a function has a local minimum?

Back

A local minimum is a point where the function value is lower than all nearby points, indicating a trough in the graph.

Front

What is the significance of x-intercepts in a polynomial function?

Back

X-intercepts are points where the function crosses the x-axis, indicating the values of x for which the function equals zero.

Front

How can you find the x-intercepts of a polynomial function?

Back

To find the x-intercepts of a polynomial function, set the function equal to zero and solve for x.

Front

What is the role of the first derivative test in determining increasing/decreasing intervals?

Back

The first derivative test helps identify intervals of increase or decrease by evaluating the sign of the derivative at critical points.

Front

What is a critical point in the context of a function?

Back

A critical point is a value of x where the first derivative is zero or undefined, indicating potential local maxima, minima, or points of inflection.

Front

What is the difference between absolute and local extrema?

Back

Absolute extrema are the highest or lowest values of a function over its entire domain, while local extrema are the highest or lowest values within a specific interval.