Question

Find the average value of the function over the given interval and all values of x in the interval for which the function equals its average value. (Round your answer to three decimal places.) f(x) = 4x3 − 3x2, [−1, 3]

Answer 1

The average value of $f(x)=4x^3-3x^2$ over [-1, 3] is

$\displaystyle\frac1{3-(-1)}\int_{-1}^3(4x^3-3x^2)\,\mathrm dx=\frac14\left(x^4-x^3\right)\bigg|_{-1}^3=\frac{(3^4-3^3)-(1+1)}4=\boxed{13}$