Average Rate of Change

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What is the Average Rate of Change?

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The Average Rate of Change of a function over an interval [a, b] is defined as the change in the function's value divided by the change in the input value, calculated as (f(b) - f(a)) / (b - a).

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How do you calculate the Average Rate of Change?

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To calculate the Average Rate of Change, use the formula: (f(b) - f(a)) / (b - a), where f is the function and [a, b] is the interval.

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What does a positive Average Rate of Change indicate?

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A positive Average Rate of Change indicates that the function is increasing over the interval.

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What does a negative Average Rate of Change indicate?

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A negative Average Rate of Change indicates that the function is decreasing over the interval.

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What is the Average Rate of Change of a linear function?

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For a linear function, the Average Rate of Change is constant and equal to the slope of the line.

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If f(x) = 3x + 2, what is the Average Rate of Change from x = 1 to x = 4?

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The Average Rate of Change is (f(4) - f(1)) / (4 - 1) = (14 - 5) / 3 = 3.

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What is the Average Rate of Change of the function f(x) = x^2 on the interval [1, 3]?

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The Average Rate of Change is (f(3) - f(1)) / (3 - 1) = (9 - 1) / 2 = 4.

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How does the Average Rate of Change relate to the slope of a secant line?

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The Average Rate of Change over an interval is equivalent to the slope of the secant line that connects the points (a, f(a)) and (b, f(b)).

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What is the Average Rate of Change of a constant function?

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The Average Rate of Change of a constant function is 0, as there is no change in the function's value.

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What is the Average Rate of Change of f(x) = -2x + 5 from x = 0 to x = 3?

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The Average Rate of Change is (f(3) - f(0)) / (3 - 0) = (-1 - 5) / 3 = -2.