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Number: MA.912.C.3

Title: Apply derivatives to solve problems.

Type: Standard

Subject: Mathematics (B.E.S.T.)

Grade: 912

Strand: Calculus

This cluster includes the following benchmarks

Code	Description
MA.912.C.3.1:	Find the slope of a curve at a point, including points at which there are vertical tangent lines.
MA.912.C.3.2:	Find an equation for the tangent line to a curve at a point and use it to make local linear approximation.
MA.912.C.3.3:	Determine where a function is decreasing and increasing using its derivative.
MA.912.C.3.4:	Find local and absolute maximum and minimum points of a function.
MA.912.C.3.5:	Determine the concavity and points of inflection of a function using its second derivative.
MA.912.C.3.6:	Sketch graphs by using first and second derivatives. Compare the corresponding characteristics of the graphs of f, f' and f".
MA.912.C.3.7:	Solve optimization problems using derivatives.
MA.912.C.3.8:	Find average and instantaneous rates of change. Explain the instantaneous rate of change as the limit of the average rate of change. Interpret a derivative as a rate of change in applications, including velocity, speed and acceleration.
MA.912.C.3.9:	Find the velocity and acceleration of a particle moving in a straight line.
MA.912.C.3.10:	Model and solve problems involving rates of change, including related rates.

Vetted resources educators can use to teach the concepts and skills in this topic.

Name	Description
Velocity of the Aucilla River:	Harley Means discusses the mathematical methods hydrologists use to calculate the velocity of rivers. Download the CPALMS Perspectives video student note taking guide.
Remote Measurement of Ice Sheet Mass via Satellite:	Watch as Don Chambers explains the role of satellites in measuring the mass of ice sheets and the connections between ice sheet mass changes and sea level. Video funded by NSF grant #: OCE-1502753. Download the CPALMS Perspectives video student note taking guide.
Analyzing Antarctic Ice Sheet Movement to Understand Sea Level Changes:	In this video, Eugene Domack explains how past Antarctic ice sheet movement rates allow us to understand sea level changes. Video funded by NSF grant #: OCE-1502753. Download the CPALMS Perspectives video student note taking guide.

Name	Description
Absolute and Relative Minima and Maxima:	You will learn how to find the absolute and relative minima and maxima of functions.
Identifying relative minimum and maximum values:	You will learn how to identify relative minimum and maximum values of functions.
Concavity, concave upwards and concave downwards intervals:	You will learn how to find concavity, concave upwards and concave downwards intervals of functions, and how this relates to the second derivative of a function.
Recognizing Concavity of Functions:	Learn how to recognizing concavity of functions.
Inflection points of functions:	How to find inflection points of functions graphically and using the second derivaive.
Graphing with Derivatives:	You will learn how to use the first and second derivatives to identify critical points and inflection points and to graph a logarithm function.

Vetted resources students can use to learn the concepts and skills in this topic.

Title	Description
Absolute and Relative Minima and Maxima:	You will learn how to find the absolute and relative minima and maxima of functions.
Identifying relative minimum and maximum values:	You will learn how to identify relative minimum and maximum values of functions.
Concavity, concave upwards and concave downwards intervals:	You will learn how to find concavity, concave upwards and concave downwards intervals of functions, and how this relates to the second derivative of a function.
Recognizing Concavity of Functions:	Learn how to recognizing concavity of functions.
Inflection points of functions:	How to find inflection points of functions graphically and using the second derivaive.
Graphing with Derivatives:	You will learn how to use the first and second derivatives to identify critical points and inflection points and to graph a logarithm function.

Standard 3 : Apply derivatives to solve problems.