# Find the point(s) at which the function f(x) = 2 - x^2 equals its average value on the...

## Question:

Find the point(s) at which the function {eq}f(x) = 2 - x^2 {/eq} equals its average value on the interval {eq}[-6,3] {/eq}.

## Average Value of a Function:

Average value of a function {eq}f(x) {/eq} over the domain {eq}\left[ a,b \right] \ {/eq}is: {eq}\displaystyle f_{avg} = \dfrac{1}{b-a} \int_{a}^{b} f(x) \ dx {/eq}.

It is given that the function equals its average value on the interval, so we'll solve the equation to get the desired solution..

## Answer and Explanation:

We are given: {eq}f(x) = 2-x^2 {/eq}

Now the average value of the function {eq}f(x) = 2- x^2 {/eq} on the given interval {eq}[- 6 , 3 ] {/eq}...

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