I am asked to find an example of a discontinuous function f : [ 0 , 1 ] → R where the intermediate value theorem fails. I went over the intermediate value theorem todayLet f : [ a , b ] → R be a continuous function. Suppose that there exists a y such that f ( a ) &lt; y &lt; f ( b ) or f ( a ) &gt; y &gt; f ( b ) . Then there exists a c ∈ [ a , b ] such that f ( c ) = y.I understand the theory behind it, however, we did not go over many example of how to use it to solve such problems so I do not really know where to begin

Question

I am asked to find an example of a discontinuous function   f  :  [  0  ,  1  ]  →      R   where the intermediate value theorem fails. I went over the intermediate value theorem todayLet   f  :  [  a  ,  b  ]  →      R   be a continuous function. Suppose that there exists a y such that   f  (  a  )  &amp;lt;  y  &amp;lt;  f  (  b  ) or   f  (  a  )  &amp;gt;  y  &amp;gt;  f  (  b  )  . Then there exists a         c  ∈  [  a  ,  b  ] such that   f  (  c  )  =  y.I understand the theory behind it, however, we did not go over many example of how to use it to solve such problems so I do not really know where to begin

grcalia1 · Accepted Answer

Look for a function with a jump discontinuity.

I am asked to find an example of a discontinuous function f : [ 0 , 1 ] &#x

Answered question

Answer & Explanation

New Questions in Calculus 2