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Mathematics
Mathematics
Problem
At the point
(
2
,
−
1
)
(2,-1)
(
2
,
−
1
)
, a curve satisfies
d
y
d
x
=
−
4
\displaystyle \frac{dy}{dx}=-4
d
x
d
y
=
−
4
and
d
2
y
d
x
2
=
6
y
−
4
x
(
d
y
d
x
)
(
3
y
−
4
x
)
2
.
\frac{d^{2}y}{dx^{2}}=\frac{6y-4x\left(\frac{dy}{dx}\right)}{(3y-4x)^{2}}.
d
x
2
d
2
y
=
(
3
y
−
4
x
)
2
6
y
−
4
x
(
d
x
d
y
)
.
Determine whether the curve is concave up or concave down at
(
2
,
−
1
)
(2,-1)
(
2
,
−
1
)
.
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