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Numerade Educator

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Problem 14 Medium Difficulty

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.

Answer

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

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Video Transcript

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