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Find the numbers $ b $ such that the average value of $ f(x) = 2 + 6x - 3x^2 $ on the interval $ [0, b] $ is equal to 3.

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$\frac{3 \pm \sqrt{5}}{2} \approx 0.382,2.618$

Calculus 2 / BC

Chapter 6

Applications of Integration

Section 5

Average Value of a Function

Missouri State University

Harvey Mudd College

University of Michigan - Ann Arbor

University of Nottingham

Lectures

02:59

Find the numbers $ b $ suc…

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Find the numbers $b$ such …

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4. Find the numbers b such…

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Determine the average valu…

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Find the average value of …

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Let's use the average value formula. The average is one over B minus a from the bounds of a which is zero to be, and then our function. We can simplify this. This gives us B squared minus three. B plus one is zero. Now we can use the quadratic formula. A is one B is negative. Three sees one b squared. We can put him so we have be scored. Mass. Three People's 102 Using the quadratic formula, we end up with three poster minus. It's word of five divided by two, which is approximately 0.3 to 2.618

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