   Chapter 2.1, Problem 55E

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# Let H ( t ) be the daily cost (in dollars) to heat an office building when the outside temperature is t degrees Fahrenheit.(a) What is the meaning of H ′ ( 58 ) ? What are its units?(b) Would you expect H ′ ( 58 ) to be positive or negative? Explain.

To determine

To explain: Meaning of H’ (58) an its unit.

Explanation

H’ (t) means rate of change of daily cost with respect to outside temperature in degrees Fahrenheit or the rate of change of cost H (t) with respect to t.

H’ (58) means rate of change in daily cost to heat an office, when temperature is 58 degrees Fahrenheit.It can be written as,

H'58=dHdtt=58

Its units Dollars / Degree Fahrenheit.

Given:The function H (t) which gives daily cost in dollars to heat an office building when the outside temperature is t degree Fahrenheit.

Conclusion: H’ (58) is the rate of change of cost with respect to temperature when temperature is 580F and its  unit is Dollars / Degree Fahrenheit.

Part (b):

To check: Whether H’ (58) is positive or negative

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