Learning Objective 2.3A

Learning Objective 2.3A Students will be able to interpret the meaning of a derivative within a problem.

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Derivatives are all over the place in science.

• Force is the derivative of momentum

• Velocity is the derivative of position

• Acceleration is the derivative of velocity

• Force is also the derivative of impulse

• Flow rate is the derivative of volume

• Marginal costs/benefits are the derivatives of costs/benefits in economics

• Derivatives can also find optimal values (the peaks and troughs we found earlier)

We'll mostly practice these in class, so our explanation here will be short.

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Essential Knowledge 2.3A1 Students will know that the unit for f '(x) is the unit for f divided by the unit for x.

Essential Knowledge 2.3A2 Students will know that the derivative of a function can be interpreted as the instantaneous rate of change with respect to its independent variable.