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Mathematics
Mathematics
Problem
Consider the function
f
(
x
)
=
{
x
+
1
,
x
≤
1
x
2
,
x
>
1
f(x)= \begin{cases} x+1, & x\le 1 \\ x^{2}, & x>1 \end{cases}
f
(
x
)
=
{
x
+
1
,
x
2
,
x
≤
1
x
>
1
On the interval
[
0
,
2
]
[0,2]
[
0
,
2
]
, do the hypotheses required for the Intermediate Value Theorem hold? Answer "yes" or "no" and state the value of
x
x
x
(if any) at which a required hypothesis fails.
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