The rate of change of the velocity with respect to time

The slope of the tangent line at a point on a curve

The process of finding the derivative of a function

A point at which the value of a function is not equal to its limit as the value of the independent variable approaches that point, or where it

An equation that contains derivatives

An integral that is indefinite

The greatest y-value of a function

The smallest y-value of a function

The value that a function is approaching as x approaches a given value from values more than x

The value that a function is approaching as x approaches a given value from values less than x

A point on the graph where the slope changes from positive to negative or vise versa

2nd derivative is negative

2nd derivative is positive

A point on the graph of the function at which the derivative is either zero or undefined

If a function is continuous over a closed interval and differentiable over an open interval from a to b and f(a) = f(b), then there exists at least one critical number in the open

If a function is continuous over a closed interval and differentiable over an open interval from a to b, then there exists a number c where the average rate of change equals the in

Allows you to find where functions are increasing and decreasing. Also allows you to find relative extrema

Allows you to find where functions are concave up or down. Also allows you to find points of inflection

A process that maximizes or minimizes a quantity

If f is continuous on [a,b], then there is a max and a min

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