The function satisfies and . But there is no between and 1 where . Why does this not violate the intermediate value theorem?
The function is defined on the interval and is continuous there. It is known that and , and these are the only values of with . It is also known that . Explain why .
The figure shows the graph of the function on the interval together with the dashed line .
and , but anywhere on . Why does this not violate the intermediate value theorem?
The figure shows only a part of the graph of the function , which is defined on all of .
If we say that for every , what can we conclude about ? Why?
The figure shows only parts of the curve .
We know that the function has the following properties: , is continuous, , and . By considering the difference , what can you conclude about this function?