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Applications of Derivatives

OPTIMIZATION

FLASH Cards!

Using an equation’s derivative to find a local/absolute maximum or minimum that identifies the ideal or best case scenario.

Optimization

RELATED RATED

Problems that use an equation and it’s derivative with respect to time to describe the way an object/ area changes over time and to predict how the object/area will behave.

Related Rates

THE EXTREME VALUE THEOREM

If a function f is continuous on [a,b] then it will have an absolute max and min.

The Extreme Value Theorem

LOCAL EXTRMA

The highest/ lowest point in a neighborhood of a graph, points where a graph changes from increasing to decreasing or decreasing to increasing. Local Extrema cannot be asymptotes

Local Extrema

ABSOLUTE EXTRMA

The highest/lowest point on a graph in a given interval. Absolute Extrema cannot be asymptotes.

Absolute Extrema

POINTS OF INFLECTION

Points where the concavity changes from positive to negative.

Points of Inflection