How do you find the point c in the interval 0 &#x2264;<!-- ≤ --> x &#x2264;<!-- ≤ --> 3

Cara Duke

Cara Duke

Answered question

2022-05-19

How do you find the point c in the interval 0 x 3 such that f(c) is equation to the average value of f ( x ) = 3 x 2 ?

Answer & Explanation

dariajoq9

dariajoq9

Beginner2022-05-20Added 14 answers

f a v e = 1 3 0 0 3 3 x 2 d x
= 1 3 [ x 3 ] 0 3
1 3 [ ( 3 3 ) ( 0 3 ) ] = 1 3 ( 27 ) = 9
Now solve
3 x 2 = 9 in [0,3]
x 2 = 3
x = ± 3 Note that the algebra gives us two solutions, but one of them is not in the interval.
c = 3

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