What is the average value of the function f(x) on the given interval [0, 16]?

To find the average value of the function f(x) over the interval [0, 16], we first need to clarify the function. Let’s assume the function is given as f(x) = x. The formula for the average value of a continuous function f over an interval [a, b] is given by:

Average Value = (1/(b – a)) * ∫_a^b f(x) dx

In our case, a = 0 and b = 16:

• Step 1: Plug in the values into the formula:
• Average Value = (1/(16 – 0)) * ∫₀¹⁶ x dx

Step 2: Now, calculate the integral:

∫₀¹⁶ x dx = [ (x²/2) ]₀¹⁶

Evaluating this gives us:

[(16²/2) – (0²/2)] = (256/2) – 0 = 128

Step 3: Now plug this back into the average value formula:

Average Value = (1/16) * 128 = 8

So, the average value of the function f(x) = x on the interval [0, 16] is 8.