Applications of Derivatives

Front

What is a relative maximum in the context of a function?

Back

A relative 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

What is a relative minimum in the context of a function?

Back

A relative 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

How do you find relative extrema of a function?

Back

To find relative extrema, take the derivative of the function, set it to zero to find critical points, and use the first or second derivative test to classify them.

Front

What is the difference between absolute extrema and relative extrema?

Back

Absolute extrema are the highest or lowest values of a function over its entire domain, while relative extrema are the highest or lowest values within a specific 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 in that interval, the function value at the second point is greater than the function value at the first point.

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 in that interval, the function value at the second point is less than the function value at the first point.

Front

What is concavity in the context of a function?

Back

Concavity refers to the direction in which a function curves: a function is concave up if it opens upwards and concave down if it opens downwards.

Front

How do you determine where a function is concave up or concave down?

Back

To determine concavity, take the second derivative of the function: if the second derivative is positive, the function is concave up; if negative, it is concave down.

Front

What is the significance of critical points in calculus?

Back

Critical points are where the derivative is zero or undefined; they are potential locations for relative extrema and points of inflection.

Front

What is a limit in calculus?

Back

A limit is a value that a function approaches as the input approaches a certain point; it helps in understanding the behavior of functions at specific points.