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Math  /  Data & Statistics

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Find the 3 unit moving average of the function f(x)=x4+8f(x)=x^{4}+8. □\square Video Example: Solving A Similar Problem

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STEP 1

1. The function given is f(x)=x4+8 f(x) = x^4 + 8 .
2. A 3-unit moving average involves averaging the function values over three consecutive integer points.

STEP 2

1. Identify the points for the moving average.
2. Calculate the function values at these points.
3. Compute the moving average for each set of three consecutive points.

STEP 3

Identify the points for the moving average. Assume we are calculating the moving average for points x=n,n+1,n+2 x = n, n+1, n+2 .

STEP 4

Calculate the function values at these points:
f(n)=n4+8 f(n) = n^4 + 8 f(n+1)=(n+1)4+8 f(n+1) = (n+1)^4 + 8 f(n+2)=(n+2)4+8 f(n+2) = (n+2)^4 + 8

STEP 5

Compute the moving average for these points:
Moving Average=f(n)+f(n+1)+f(n+2)3 \text{Moving Average} = \frac{f(n) + f(n+1) + f(n+2)}{3}
Substitute the function values:
Moving Average=n4+8+(n+1)4+8+(n+2)4+83 \text{Moving Average} = \frac{n^4 + 8 + (n+1)^4 + 8 + (n+2)^4 + 8}{3}
Simplify the expression:
Moving Average=n4+(n+1)4+(n+2)4+243 \text{Moving Average} = \frac{n^4 + (n+1)^4 + (n+2)^4 + 24}{3}
The 3-unit moving average of the function f(x)=x4+8 f(x) = x^4 + 8 is:
n4+(n+1)4+(n+2)4+243 \frac{n^4 + (n+1)^4 + (n+2)^4 + 24}{3}

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