What is the average value of the continuous linear function f(x) = 3x + 2 on the closed interval [0, 4]?
Answer and explanation
Correct answer: B. 8
The average value of a function is given by f_avg = (1 / (b - a)) integral_{a}^{b} f(x) dx. Here a = 0 and b = 4: f_avg = (1 / 4) integral_{0}^{4} (3x + 2) dx = (1 / 4) [3x^2 / 2 + 2x]_{0}^{4} = (1 / 4) [(3 16 / 2) + 2(4)] = (1 / 4) [24 + 8] = (1 / 4) * 32 = 8.
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