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Mathematics
Problem
Find the constants
A
A
A
and
B
B
B
so that
g
(
x
)
=
{
A
x
2
+
B
x
+
3
,
x
<
1
,
4
x
−
5
,
x
≥
1
g(x)= \begin{cases} Ax^{2}+Bx+3, & x<1,\\ 4x-5, & x\ge 1 \end{cases}
g
(
x
)
=
{
A
x
2
+
B
x
+
3
,
4
x
−
5
,
x
<
1
,
x
≥
1
is both continuous and differentiable at
x
=
1
x=1
x
=
1
.
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