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Mathematics
Mathematics
Problem
Let
f
(
x
)
=
{
x
2
,
x
≤
1
,
2
x
−
1
,
x
>
1.
f(x)=\begin{cases} x^2, & x\le 1,\\ 2x-1, & x>1. \end{cases}
f
(
x
)
=
{
x
2
,
2
x
−
1
,
x
≤
1
,
x
>
1.
Determine whether
f
f
f
is differentiable at
x
=
1
x=1
x
=
1
. If it is, state the value of
f
′
(
1
)
f'(1)
f
′
(
1
)
; if it is not, state that the derivative does not exist.
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