Average Value of a Function (Leaving Cert Mathematics): Quizzes

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Average Value of a Function
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What does the average value of a function provide over an interval?

A single representative value

What is the formula for average value of f(x)f(x) on [a,b][a,b]?

1b−a∫abf(x) dx\frac{1}{b-a} \int_a^b f(x) \, dx

What does ∫abf(x) dx\int_a^b f(x) \, dx represent in the average value formula?

Total area under the curve

What does b−ab-a represent in the average value formula?

Length of the interval

How is favgf_{\text{avg}} geometrically interpreted?

Constant height enclosing same area

In which fields is the average value of a function applied?

Physics, engineering, and economics

What is the average value of f(x)=2x+3f(x) = 2x + 3 on [1,4][1,4]?

88

What is the average value of f(x)=x2f(x) = x^2 on [0,3][0,3]?

33

What term describes what the average value determines about the graph?

Mean height

What is the first step when calculating average value?

Identify interval [a,b][a,b] and function

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