Let be continuous on and let denote its average value on this interval

MATHEMATICS · Single correct · ISC · Mathematics · Calculus · Calculus

Problem

Let

f

be continuous on

[2,6]

and let

\bar f

denote its average value on this interval. Which statement is always true? (a) The area under

y=f(x)

from

2

6

equals

4\,\bar f^{2}

. (b) There exists at least one

c\in(2,6)

such that

f(c)=\bar f

. (c) The point

(4,\,\bar f)

lies on the graph of

f

. (d)

\bar f

is always greater than

f(2)

and less than

f(6)