Find the average value of the function f ( x ) = 4x^4 on the interval 2 ≤ x ≤ 4

Answer 1

Greetings! Lets solve this shall we ?

So, we must find the average value of the given function which implies the average rate of change between the given interval. Then, the formula yields

[f(b) - f(a)] / (b - a), where [a, b] = [2, 4] with f(4) = 4(4)⁴ = 1024 and f(2) = 4(2)⁴ = 64. Then,

[1024 - 64] / (4 - 2) = 960 / 2 = 480

I hope this helped!

Answer 2

You can evaluate the average value of a function using the following:

1/(b-a) ∫f(x) dx evaluated at the end points.

For your problem, a = 2, b = 4

1/(4-2) ∫ 4x^4dx evaluated at 2 and 4

1/2 (4/5x^5) evaluated at 2 and 4

1/2 [(4/5(4)^5) - (4/5(2)^5)]

1/2(819.2 - 25.6)

1/2(793.6)

395.8