Anyone know how to go about this problem?!

Calculate the 5-unit moving average of the function. Plot the function and its moving average on the same graph, as in Example 4. (You may use graphing technology for the plot, but you should compute the moving average analytically.)

Question

Anyone know how to go about this problem?!

Calculate the 5-unit moving average of the function. Plot the function and its moving average on the same graph, as in Example 4. (You may use graphing technology for the plot, but you should compute the moving average analytically.)

anonymous · Answer

f(x)=(x^2/3)

john_es · Answer

The n-unit moving average of a function f(t) is defined by
$$f(x)=\int_{x-n}^xf(t)dt$$
In this case,
$$f(x)=\int_{x-5}^x(t^2/3)dt=x^3/9-(x-5)^3/9$$

john_es · Answer

The plot, http://www.wolframalpha.com/input/?i=Plot%20x%5E3%2F9-(x-5)%5E3%2F9&t=crmtb01 Also you can simplify the result, $$f(x)=125/9 - 25 x/3 + 5 x^2/3$$

anonymous · Answer

Thank you So much!