Question

The average rate of change of the function: f(x)=4x^3-3x^2+2x-1 in the interval [0,3] will be

Answer 1

29

Explanation:

The average rate of change of f(x) in the closed interval [ a, b ] is

`(f(b)-f(a))/(b-a)`

Here [ a, b ] = [ 0, 3 ], thus

f(b) = f(3) = 4(3)³ - 3(3)² + 2(3) - 1 = 108 - 27 + 6 - 1 = 86

f(a) = f(0) = - 1, thus

average rate of change =
`(86-(-1))/(3-0)` =
`(87)/(3)` = 29