the average temperature in Hartford can be expressed as t = f(m) where m is month (January = 1, etc.) and t is the average daily high temperature for the month in degrees F.
1) what is the meaning of f'(m)?
rate of change of the average temperature (in degrees F) as the month changes.
2) what are the units?
temperature/month
3) is f'(3) positive or negative? why?
positive because march is a month where the temperature gets warmer
4) what does it mean to say f'(7)=0?
in month 7 the average temperature stayed the same as the previous month
are my answers correct?
#2 more properly, °F/mo
otherwise, they look good.
Yes, your answers are correct!
1) The meaning of f'(m) is the rate of change of the average temperature (in degrees F) as the month changes. In other words, it represents how fast the average temperature is increasing or decreasing as the month value changes.
2) The units of f'(m) would be temperature per month, as it measures the change in temperature (in degrees F) for each increase in the month value.
3) Since f'(m) represents the rate of change of the average temperature, if f'(3) is positive, it means that as the month increases from 2 to 3 (from February to March), the average temperature is increasing. This is because March is generally a month where the temperature gets warmer.
4) If f'(7) = 0, it means that in the 7th month (July), the average temperature did not change compared to the previous month. There was no increase or decrease in the average temperature during this month.