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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 ...

Power Function Derivative

"The derivative of a power function involving x to the nth power (n being non-zero) can be derived using the definition of the derivative. The power function derivative is equal to x to the (n-1)th po ...

Polynomial Derivatives

"The derivative of a polynomial function involving multiple linear and/or power functions can be found using the formulas for finding linear and power functions, along with the constant multiple and s ...

Computing Definite Integrals using Substitution

"Definite integrals, like their relatives indefinite integrals, can sometimes be solved by using substitution. When computing definite integrals using substitution, the limits of the integral must be ...

Complicated Indefinite Integrals

"Not all indefinite integrals follow one simple rule. Some are slightly more complicated, but they can be made easier by remembering the derivatives they came from. These complicated indefinite integr ...

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