Find the 4 unit moving average of the function $g(x)=15-x^{3}$.
Answer
Final Answer: The 4 unit moving averages of the function \(g(x)=15-x^{3}\) over the intervals from -10 to 10 are \(\boxed{559}\), \(\boxed{95}\), \(\boxed{15}\), \(\boxed{-65}\), and \(\boxed{-529}\) respectively.
Step 1 ：We are asked to find the 4 unit moving average of the function \(g(x)=15-x^{3}\). This means we need to find the average value of the function over each 4 unit interval.
Step 2 ：We can use the formula for the moving average of a function over an interval [a, b]: \(\frac{1}{b-a}\int_{a}^{b}f(x)dx\). In this case, the interval is 4 units, so \(b-a=4\). We can calculate the moving average for each 4 unit interval by integrating the function over that interval and dividing by 4.
Step 3 ：The 4 unit moving averages of the function \(g(x)=15-x^{3}\) over the intervals from -10 to 10 are calculated to be 559, 95, 15, -65, and -529 respectively.
Step 4 ：Final Answer: The 4 unit moving averages of the function \(g(x)=15-x^{3}\) over the intervals from -10 to 10 are \(\boxed{559}\), \(\boxed{95}\), \(\boxed{15}\), \(\boxed{-65}\), and \(\boxed{-529}\) respectively.
