MA.912.C.3: Apply derivatives to solve problems.

Apply derivatives to solve problems.

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