AP Calculus AB / Applications of Integration / Question No. 41

41. Find the number(s) \( b \) such that the average value of \[ y = 2 + 6x - 3x^2 \] on the interval \( [0, b] \) is equal to 3.

Hint: Use the formula for average value and the quadratic formula. What is the correct value of \( b \)?

\( \frac{3 \pm \sqrt{5}}{2} \)

\( \frac{3 \pm \sqrt{13}}{2} \)

\( \frac{5 \pm \sqrt{3}}{2} \)

\( \frac{2 \pm \sqrt{7}}{3} \)

Answer is: option1

\( \frac{3 \pm \sqrt{5}}{2} \)

Solution:

\( \frac{3 \pm \sqrt{5}}{2} \)

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