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Mathematics
Mathematics
Problem
At a point on an implicitly defined curve where
d
y
d
x
=
0
\dfrac{dy}{dx}=0
d
x
d
y
=
0
, which of the following conditions on
d
2
y
d
x
2
\dfrac{d^{2}y}{dx^{2}}
d
x
2
d
2
y
most strongly indicates a local maximum of
y
y
y
with respect to
x
x
x
? a)
d
2
y
d
x
2
>
0
\dfrac{d^{2}y}{dx^{2}}>0
d
x
2
d
2
y
>
0
b)
d
2
y
d
x
2
<
0
\dfrac{d^{2}y}{dx^{2}}<0
d
x
2
d
2
y
<
0
c)
d
2
y
d
x
2
=
0
\dfrac{d^{2}y}{dx^{2}}=0
d
x
2
d
2
y
=
0
d) The sign of
d
2
y
d
x
2
\dfrac{d^{2}y}{dx^{2}}
d
x
2
d
2
y
is irrelevant
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