How do you find the point c in the interval 0 &#x2264;<!-- ≤ --> x &#x2264;<!-- ≤ --> 2

Villaretq0

Villaretq0

Answered question

2022-06-22

How do you find the point c in the interval 0 x 2 such that f(c) is equation to the average value of f ( x ) = 2 x ?

Answer & Explanation

lodosr

lodosr

Beginner2022-06-23Added 24 answers

Explanation:
The average value of a function f on interval [a,b] is
1 b a a b f ( x ) d x
So we need to find the average value, then solve the equation
f(x) = average value on the interval [a,b] If the equation has more than one solution then c can be any one of the solutions in [a,b]
In this question we get
Solve: 2 x = 1 2 0 0 2 2 x d x
Evaluating the integral gets us:
Solve: 2 x = 4 3
The only solution is x = 8 9

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