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The temperature, $H$ , in degrees Celsius, of a hot cup of coffee placed on the kitchen counter is given by $H = f(t)$ , where $t$ represents the number of minutes since the coffee was put on the counter.

(a) Choose the correct word to complete the sentence. Be sure you can give a reason for your choice:

If $t>0$ then $f'(t)$ is
positive. negative. zero.

If you are using MathQuill then click the textbox (Tt) button before entering the answer to part (b).

(b) What are the units of $f'(10)$ ? units

(c) Suppose that $\lvert f'(10) \rvert = 0.4$ and $f(10) = 67$ . Fill in the blanks, including units where needed, and select the appropriate terms to complete the following statement about the temperature of the coffee in this case.

At minutes after the coffee was put on the counter, its is and will by about in the next 75 seconds.

You can earn partial credit on this problem.