How do you find the point c in the interval

Gretchen Schwartz

Gretchen Schwartz

Answered question

2022-07-08

How do you find the point c in the interval 4 x 6 such that f(c) is equation to the average value of f(x)=2x?

Answer & Explanation

Keegan Barry

Keegan Barry

Beginner2022-07-09Added 18 answers

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(c)=average value on the interval [a,b]
For our case we get
Solve:
2 c = 1 6 ( 4 ) 4 6 ( 2 x ) d x
Evaluating the integral we get:
Solve: 2c=2
The only solution is c=1

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