AP Calculus ABhardmcq1 pt

The temperature TT of a cup of coffee is cooling in a room, modeled by the function T(t)T(t), where TT is measured in degrees Celsius and tt is measured in minutes. Which of the following expressions represents the average rate of change of the coffee's temperature between t=2t = 2 and t=10t = 10 minutes?

A.T(10)T(2)102\frac{T(10) - T(2)}{10 - 2}
B.T(10)T(2)T'(10) - T'(2)
C.T(10)T(2)102\frac{T'(10) - T'(2)}{10 - 2}
D.T(10)T(2)T(10) - T(2)

Explanation

Core Concept

Correct. The average rate of change of a function over an interval [a,b][a, b] is given by the difference quotient f(b)f(a)ba\frac{f(b) - f(a)}{b - a}.

Correct Answer

AT(10)T(2)102\frac{T(10) - T(2)}{10 - 2}

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