The average value of a function f(x) = 4 - x² is 2.67 and for x = 1.15 the function equals its average value.
In this question, we have been given a function f(x) = 4 - x^2
We need to find the average value of the function over the given interval , [-2, 2]
We know that the average value of a function f(x) from x=a to x=b is given by
A = 1/(b-a) * integral from a to b of f(x)
For given function,
A = 1/(2 - (-2)) * ∫_[-2, 2] (4 - x²)dx
A = 1/4 * [4x - x³/3]_(-2) to 2
A = 1/4 * 10.66
A = 2.67
Now we need to find the interval for which the function equals its average value.
We need to find the value of x for which f(x) = 2.67
4 - x² = 2.67
x² = 4 - 2.67
x² = 1.33
x = 1.15
Therefore, the average value of a function is 2.67 and for x = 1.15 the function equals its average value.
Learn more about the function here:
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