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Mathematics
Mathematics
Problem
Consider the function
f
(
x
)
=
{
a
x
2
+
b
x
+
2
,
x
<
1
x
+
3
,
x
≥
1
f(x)=\begin{cases} ax^{2}+bx+2, & x<1\\ \sqrt{x+3}, & x\ge 1 \end{cases}
f
(
x
)
=
{
a
x
2
+
b
x
+
2
,
x
+
3
,
x
<
1
x
≥
1
For which ordered pair
(
a
,
b
)
(a,b)
(
a
,
b
)
is
f
f
f
both continuous and differentiable at
x
=
1
x=1
x
=
1
? a)
(
1
2
,
−
1
2
)
\left(\dfrac12,\,-\dfrac12\right)
(
2
1
,
−
2
1
)
b)
(
1
4
,
−
1
4
)
\left(\dfrac14,\,-\dfrac14\right)
(
4
1
,
−
4
1
)
c)
(
−
1
4
,
1
4
)
\left(-\dfrac14,\,\dfrac14\right)
(
−
4
1
,
4
1
)
d)
(
0
,
1
4
)
\left(0,\,\dfrac14\right)
(
0
,
4
1
)
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