#### To determine

The meaning of H′(8) and its units.

#### Explanation

The function H(t) be the daily cost (in dollars) to heat an office building when the outside temperature is *t*

Note that, the derivative f′(x) is the instantaneous rate of change of the function f(x) with respect to *x*

The derivative H′(t) is rate of change of daily cost (in dollars) to heat an office building with respect to when the outside temperature is *t*

The derivative H′(58) is rate of change of daily cost (in dollars) to heat an office building with respect to when the outside temperature is 58°F.

The instantaneous rate of change is equal to H′(t)=limΔx→0ΔyΔt here y=H(t).

Here Δy is measured in dollars and Δt is measured in degree Fahrenheit.

Thus, the units are dollars per degree Fahrenheit.

#### To determine

The value H′(58)

#### Explanation

Here the outside temperature is 58° F.

The building should require less heating when the outside temperature increases,

Thus, the daily cost to heat the office building is less when the outside temperature 58° F

Therefore, the expecting value of H′(58) is negative.