MHB What Does the Intermediate Value Theorem Guarantee for a Continuous Function?

[karush]

I thot I posted this before but couldn't find it ... if so apologize

Let f be a function that is continuous on the closed interval [2,4] with $f(2)=10$ and $f(4)=20$
Which of the following is guaranteed by the $\textbf{Intermediate Value Theorem?}$

$a.\quad f(x)=13 \textit{ has a least one solution interval } (2,4)$
$b.\quad f(3)=f(15)$
$c. \quad \textit{f attains a maximum on the open interval } (2,4)$
$d.\quad f'(x)=5 \textit{ has at least one solution in the open interval }(2,4)$
$e. \quad f'(x)>0\textit{ for all x in the open interval }(2,4)$

 

[skeeter]

looks like dashes in multiple places where equal signs should be

a. $f(x)=13$ has at least one solution in the interval $(2,4)$

is the correct choice.

https://www.mathsisfun.com/algebra/intermediate-value-theorem.html