Front

What is the derivative of a function?

Back

The derivative of a function measures how the function's output value changes as its input value changes. It represents the slope of the tangent line to the graph of the function at a given point.

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's value at the second point is greater than its value at the first point.

Front

What is a relative maximum?

Back

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

Front

What is a relative minimum?

Back

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

Front

What is a point of inflection?

Back

A point of inflection is a point on the graph of a function where the concavity of the function changes.

Front

How do you find the second derivative of a function?

Back

To find the second derivative, take the derivative of the first derivative of the function.

Front

What does it mean for a function to be differentiable?

Back

A function is differentiable at a point if it has a derivative at that point, meaning it is smooth and has no sharp corners or discontinuities.

Front

What is the relationship between the first derivative and the increasing/decreasing behavior of a function?

Back

If the first derivative is positive, the function is increasing; if the first derivative is negative, the function is decreasing.

Front

What is the significance of the second derivative?

Back

The second derivative indicates the concavity of the function: if it is positive, the function is concave up; if negative, concave down.

Front

How do you determine critical points of a function?

Back

Critical points occur where the first derivative is zero or undefined.