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Mathematics
Mathematics
Problem
Consider the piecewise function
g
(
x
)
=
{
c
x
2
+
d
,
x
<
1
ln
x
,
x
≥
1
g(x)=\begin{cases} cx^{2}+d, & x<1 \\ \ln x, & x\ge 1 \end{cases}
g
(
x
)
=
{
c
x
2
+
d
,
ln
x
,
x
<
1
x
≥
1
Which ordered pair
(
c
,
d
)
(c,d)
(
c
,
d
)
makes
g
g
g
both continuous and differentiable at
x
=
1
x=1
x
=
1
? a)
(
1
,
−
1
)
(1,-1)
(
1
,
−
1
)
b)
(
1
2
,
0
)
\left(\dfrac12,0\right)
(
2
1
,
0
)
c)
(
1
2
,
−
1
2
)
\left(\dfrac12,-\dfrac12\right)
(
2
1
,
−
2
1
)
d)
(
0
,
0
)
(0,0)
(
0
,
0
)
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