Intervals of Increase, Decrease, Constant; min and max points

Front

What is a relative maximum?

Back

A relative maximum is a point on a graph where the function value is higher 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 minimum point?

Back

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

Front

What is an inflection point?

Back

An inflection point is a point on a curve where the curvature changes sign, indicating a change in the direction of the curve.

Front

How do you identify intervals of increase?

Back

Intervals of increase are sections of the graph where the function values rise as x increases.

Front

How do you identify intervals of decrease?

Back

Intervals of decrease are sections of the graph where the function values fall as x increases.

Front

What does it mean for a function to be constant?

Back

A function is constant on an interval if it does not change value; the graph is a horizontal line.

Front

How can you find relative maxima and minima on a graph?

Back

Relative maxima and minima can be found by identifying the highest and lowest points in a given interval.

Front

What is the significance of critical points?

Back

Critical points are where the derivative is zero or undefined, indicating potential maxima, minima, or inflection points.

Front

What is the first derivative test?

Back

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