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**1. Homework Statement**

Suppose that t hours after a piece of food is put in the fridge its temperature (in Celsius) is

T(t) = 15 - 3t + [tex]\frac{4}{t - 1}[/tex]

where 0 [tex]\leq[/tex] t [tex]\leq[/tex] 5.

Find the rate of change of temperature after one hour.

**3. The Attempt at a Solution**

Since it's asking for rate of change, I'm guessing I have to find the derivative of the equation with respect to t.

T(t) = 15 - 3t + [tex]\frac{4}{t - 1}[/tex]

T`(t) = 0 - 3 + [tex]\frac{0(t - 1) - 1(4)}{(t-1)^{2}}[/tex]

*(Quotient Rule)*

T`(t) = -3 + [tex]\frac{0 - 4}{(t-1)^{2}}[/tex]

T`(t) = -3 + [tex]\frac{-4}{(t-1)^{2}}[/tex]

T`(t) = -3 - [tex]\frac{4}{(t-1)^{2}}[/tex]

Would I just plug in 1 after this?