Calculus question

[sephisel]

Hello,
In advance I want to thank all those that try to help me.

Question is:
Suppose that f(T) represents the daily cost to heat a certain house in dollars when the mean outside temperature is T degrees Fahrenheit, 40<= T <=60.
Give a physical interpretation, with units specified, of the statement f ' (50) = -0.15.

I don't know where to start with this question.

 

[Deleted member 4993]

Hello,
In advance I want to thank all those that try to help me.

Question is:
Suppose that f(T) represents the daily cost to heat a certain house in dollars when the mean outside temperature is T degrees Fahrenheit, 40<= T <=60.
Give a physical interpretation, with units specified, of the statement f ' (50) = -0.15.

I don't know where to start with this question.

I'll give you part of the interpretation:

f'(T) is negative - that means - as T (the mean outside temperature) increases, the amount of money spent to heat the house [f(T)] decreases.

Makes sense!!

Now tell us - what else does that statement tell you?

 

[Bob Brown MSEE]

Hello,
In advance I want to thank all those that try to help me.

Question is:
Suppose that f(T) represents the daily cost to heat a certain house in dollars when the mean outside temperature is T degrees Fahrenheit, 40<= T <=60.
Give a physical interpretation, with units specified, of the statement f ' (50) = -0.15.

I don't know where to start with this question.

All you can say is that at 50 ^ᵒF it is cheaper to heat by 15 cents per ^ᵒF of outside temperature.
You can't say if that continues to be true over the entire interval.

There are several assumptions that allow you to say more
1) Newton's Law of cooling applies
2) Some boundry condition
3) Pricing structure for heating and units (i.e. $/Joule etc)

The point is that we don't know the house, an air conditioner could kick in destroying the behavior modeled by Newton's Law. Look for other statements about assumptions or apply assumptions normally used in your class.