Florida B.E.S.T. MA.912.C.3

MA.912.C.3 is a B.E.S.T. standard. These are the benchmarks under it.

• 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.3.10

  Model and solve problems involving rates of change, including related rates.

• 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...

• MA.912.C.3.9

  Find the velocity and acceleration of a particle moving in a straight line.

01

What Students Need to Do

Students use derivatives to find rates of change, intervals of increase or decrease, and maximum or minimum values. They build and interpret models for motion, optimization, and other applied situations.

02

What Mastery Looks Like

Students choose a useful variable, write a function, and use its derivative to answer the question. They check critical points and endpoints when needed. They explain the result with correct units and context.

03

Common Misconceptions

Students may assume every point where the derivative is zero is a maximum or minimum. They often ignore endpoints, confuse position with velocity, or drop units. Some optimize the wrong quantity because they do not define variables first.

04

How to Assess It

Give this exit ticket: A farmer has 40 meters of fencing for three sides of a rectangular pen beside a barn. Write the area function, use its derivative, and find the dimensions that maximize area.

1. 01

   Roll a toy car down a ramp, record position over time, and use secant slopes to estimate its instantaneous velocity.

2. 02

   Ask students to explain why a zero derivative does not always prove that a maximum or minimum occurs.

3. 03

   Run a card sort matching functions, derivative signs, graphs, and claims about increasing, decreasing, maximum, and minimum values.

4. 04

   Use a cardboard box net to find the corner cut size that produces the greatest possible volume.

• MA.912.LT.1

  Apply recursive methods to solve problems.

• MA.912.C.2

  Develop an understanding for and determine derivatives.

• MA.912.C.5

  Apply integrals to solve problems.