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Mathematics
Mathematics
Problem
Consider the piecewise function
f
(
x
)
=
{
x
2
−
4
x
+
3
,
x
<
1
,
a
x
+
b
,
x
≥
1.
f(x)=\begin{cases} x^{2}-4x+3, & x<1,\\ ax+b, & x\ge 1. \end{cases}
f
(
x
)
=
{
x
2
−
4
x
+
3
,
a
x
+
b
,
x
<
1
,
x
≥
1.
Which pair
(
a
,
b
)
(a,b)
(
a
,
b
)
ensures that
f
f
f
is differentiable at
x
=
1
x=1
x
=
1
? a)
a
=
−
2
,
b
=
−
2
a=-2,\; b=-2
a
=
−
2
,
b
=
−
2
b)
a
=
2
,
b
=
−
2
a=2,\; b=-2
a
=
2
,
b
=
−
2
c)
a
=
−
2
,
b
=
2
a=-2,\; b=2
a
=
−
2
,
b
=
2
d)
a
=
−
1
,
b
=
1
a=-1,\; b=1
a
=
−
1
,
b
=
1
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