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Derivative Definition

"The definition of the derivative is the slope of a line that lies tangent to the curve at the specific point. The limit of the instantaneous rate of change of the function as the time between measure ...

Definite Integrals as Net Change

"Definite integrals can be used to find the net change in a function between two times. The fundamental theorem of Calculus can be restated so that the definite integral of the function's derivative i ...

Definite Integrals and Area

"Definite integrals can be used to find the area under, over, or between curves. If a function is strictly positive, the area between it and the x axis is simply the definite integral. If it is simply ...

Quotient Rule

"The quotient rule is useful when trying to find the derivative of a function that is divided by another function. As long as both functions have derivatives, the quotient rule tells us that the final ...

Curve Sketching

"Sketching a curve from knowledge of the signs of the first and second derivatives is a useful way to find the approximate shape of a function's graph. When curve sketching making a sign chart of the ...

Critical Points

"Critical points are places where the derivative of a function is either zero or undefined. These critical points are places on the graph where the slope of the function is zero. All relative maxima a ...

Cost and Revenue

"One of the most important parts of economics is knowing the revenues and costs and how they relate to increased production. These can both be modeled by functions. These cost and revenue functions ca ...

Product Rule

Hipervinculo Matemáticas

Product Rule

"Use the product rule to find the derivative of the product of two functions--the first function times the derivative of the second, plus the second function times the derivative of the first. The pr ...

Continuous Functions

"In order for a function to have continuity at a certain point, several conditions including (1) the existence of the point in the domain and (2) the existence of a two-sided limit as the point approa ...

Continuity of a Function

"In order for a function to be continuous at a certain point, three conditions must be met: (1) that the point is in the domain of the function, (2) that the two-sided limit of the function as it appr ...

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