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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 ...

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 ...

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 ...

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 ...

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 ...

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 ...

Closed Interval Method

"The closed interval method is a way to solve a problem within a specific interval of a function. The solutions found by the closed interval method will be at the absolute maximum or minimum points on ...

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