Interpreting Derivatives and Integrals (UNITS!)

• I have a great understanding of units!

• I sometimes understand units

• I need to REALLY work on units

• Let's Practice!

• Let's Practice!

If s(t) represents the meters traveled in t minutes, s'(t) would represent...

• meters

• meters/min

• meters/min^2

• min/meters

The function W(t) gives the pool's water level (in gal) after t hours. W'(t) units would be...

• gallons

• gallons/hour

• gallons/hour^2

• hour/gallons

 t is measured in minutes and temperature H(t) is measured in degrees Celsius, What would the units be if we found

 $\frac{1}{10}\int_0^{10}H\left(t\right)dt$  

• Degrees Celsius

• Degrees Celsius/minute

• Degrees Celsius^2

• Degrees Celsius/minute^2

 t is measured in minutes and temperature H(t) is measured in degrees Celsius, What would the units be if we found H'(7)?

• Degrees Celsius

• Degrees Celsius/minute

• Degrees Celsius^2

• Degrees Celsius/minute^2

The table gives values of the rate of change of the radius of the balloon, r(t), measured in feet per minute. What would the units be if you found r'(9)

• ft

• ft/min

• ft/min^2

• min/ft

The table gives values of the rate of change of the radius of the balloon, r(t), measured in feet per minute. What would the units be if you found a LRAM to approximate $\int_1^{12}r\left(t\right)dt$  

• ft

• ft/min

• ft/min^2

• min/ft

The table gives values of the rate of change of the radius of the balloon, r(t), measured in feet per minute. What would the units be if you found the average value of r(t) from 0 to 12. 

• ft

• ft/min

• ft/min^2

• min/ft

Water is pumped into a tank at a rate modeled by W(t) liters per hour, where t is measured in hours. If you found W'(t), the units would be...

• liters

• liters/hr

• liters/hr^2

• hrs/liter