Essential Knowledge 2.3A1

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

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The description of the Essential Knowledge pretty much speaks for itself. Let's just look at a few examples.

Example 1

Let's go all the way back to that position function of a ball dropped from a building 1000 feet in the air

f(t) = 1000 - 16t²

In this equation, the unit for t, time, is seconds. The unit for f(t), position, is feet. As stated in the description "Students will know that the unit for f '(x) is the unit for f divided by the unit for x." In other words, feet/sec. Therefore it's no surprise that for our new equation

f'(t) = -32t²

f'(t) measures velocity, which has the units of feet per second.

Example 2

Using data collected studying how much used cars sell for, one can make a graph of the value of a car with a certain milage. Here's an example.

Let's simplify things quite a bit. Let's say I bought a car for $20,000. Let's pretend the equation is

V = -0.06x + 20,000

Where V is the worth of the car in dollars, and x is the miles driven. If you take the derivative

Q = 0.06

Where Q is the loss of value per mile. The units will be the units of V ($) divided by the units of x (mile). And thus our equation tells us that for every mile you drive, your car is worth $0.06 less.