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Mathematics
Problem
Consider the curve
x
2
−
x
y
+
y
2
=
3
x^{2}-xy+y^{2}=3
x
2
−
x
y
+
y
2
=
3
. With respect to
x
x
x
, the curve at the point
(
1
,
1
)
(1,1)
(
1
,
1
)
is a) concave up because
d
2
y
d
x
2
>
0
\dfrac{d^{2}y}{dx^{2}}>0
d
x
2
d
2
y
>
0
there b) concave down because
d
y
d
x
<
0
\dfrac{dy}{dx}<0
d
x
d
y
<
0
there c) concave down because
d
2
y
d
x
2
<
0
\dfrac{d^{2}y}{dx^{2}}<0
d
x
2
d
2
y
<
0
there d) a point of inflection because
d
2
y
d
x
2
=
0
\dfrac{d^{2}y}{dx^{2}}=0
d
x
2
d
2
y
=
0
there
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