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Mathematics
Mathematics
Problem
A function
h
h
h
is defined by
h
(
x
)
=
{
a
x
2
+
b
,
x
<
2
(
x
−
2
)
(
a
+
b
)
+
5
,
x
≥
2
h(x)=\begin{cases} ax^{2}+b,& x<2\\ (x-2)(a+b)+5,& x\ge 2 \end{cases}
h
(
x
)
=
{
a
x
2
+
b
,
(
x
−
2
)
(
a
+
b
)
+
5
,
x
<
2
x
≥
2
The function is required to be both continuous and differentiable at
x
=
2
x=2
x
=
2
. Which ordered pair
(
a
,
b
)
(a,b)
(
a
,
b
)
satisfies these conditions? a)
(
1
,
1
)
(1,1)
(
1
,
1
)
b)
(
5
11
,
35
11
)
\left(\dfrac{5}{11},\dfrac{35}{11}\right)
(
11
5
,
11
35
)
c)
(
5
7
,
15
7
)
\left(\dfrac{5}{7},\dfrac{15}{7}\right)
(
7
5
,
7
15
)
d)
(
1
,
3
)
(1,3)
(
1
,
3
)
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