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Intervals of Increase and Decrease

"Finding intervals of increase and decrease of a function can be done using either a graph of the function or its derivative. These intervals of increase and decrease are important in finding critical ...

Instantaneous Rate of Change

"The instantaneous rate of change is the rate of change of a function at a certain time. If given the function values before, during, and after the required time, the instantaneous rate of change can ...

Inflection Points

"Inflection points are points on the graph where the concavity changes. A positive second derivative means a function is concave up, and a negative second derivative means the function is concave down ...

Important Limits

"An important limit in calculus, which is central to finding derivatives of exponential functions, involves finding the limit as h approaches 0 of a special function. This limit, one of a few importan ...

The Derivative Function

"By definition, the derivative is a function which is derived from another function. The definition of the derivative is usually only written for one point, but the function is defined for all points. ...

Substitution Method

"The substitution method is a very valuable way to evaluate some indefinite integrals. The substitution method adds a new function into the one being integrated, and substitutes the new function and i ...

General Power Rule

"The general power rule is a special case of the chain rule. It is useful when finding the derivative of a function that is raised to the nth power. The general power rule states that this derivative ...

First Derivative Test

"The first derivative test is a way to find if a critical point of a continuous function is a relative minimum or maximum. Simply, if the first derivative is negative to the left of the critical point ...

Exponential Rule

"The exponential rule is a special case of the chain rule. It is useful when finding the derivative of e raised to the power of a function. The exponential rule states that this derivative is e to the ...

Second Derivative Test

"The second derivative test is useful when trying to find a relative maximum or minimum if a function has a first derivative that is zero at a certain point. Since the first derivative test fails at t ...

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