document.write( "Question 789294: Let f be continuous where f(2)=-4 and f(11)=9. Classify the statement as always, sometimes or never true.
\n" ); document.write( "There exists c in (2,11) such that f(c)=20. \n" ); document.write( "

Algebra.Com's Answer #478813 by fcabanski(1391) $\"\"$ $\"About$

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This is sometimes true.

\n" ); document.write( "The Intermediate Value Theorem states that if f is continuous on a closed interval [a,b], f(a) does not equal f(b), and k is any number between f(a) and f(b), then there is at least one number c in [a,b] such that f(c)=k.

\n" ); document.write( "In this case f(c) =k is not between f(2) and f(11). For a sin function, for example, this could be true. For a straight line function, it is false. So it's sometimes true.

\n" ); document.write( "Note the problem may not be written correctly. It indicates that f is continuous at the end points. It does not specify that the function is continuous in the interval [a,b]. If that's intentional, then the answer is still sometimes true.
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