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Risorse educative > calculo

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Velocity and Acceleration

"If position is given by a function p(x), then the velocity is the first derivative of that function, and the acceleration is the second derivative. By using differential equations with either velocit ...

Using the Second Derivative Test

"Some optimization problems can be solved by use of the second derivative test. If the second derivative is always positive, the function will have a relative minimum somewhere. If it is always negati ...

Using the First Derivative Test

"Some optimization problems use the first derivative test to find an absolute minimum or maximum. Using the first derivative test requires the derivative of the function to be always negative on one s ...

Tricky Substitutions Involving Radicals

"When an indefinite integral involves a function of x times the radical of another function of x, the substitution method must be used in multiple ways. In these tricky substitutions involving radical ...

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 ...

Infinite Limits

"When a Calculus limit decreases or increases without bound near certain values for the independent variables, we call these infinite limits. In general, a fractional function will have an infinite li ...

Indefinite Integrals

"Indefinite integrals are functions that do the opposite of what derivatives do. They represent taking the antiderivatives of functions. A formula useful for solving indefinite integrals is that the i ...

Indefinite Integral

"An indefinite integral is a function that takes the antiderivative of another function. It is visually represented as an integral symbol, a function, and then a dx at the end. The indefinite integral ...

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