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Mathematics
Mathematics
Problem
Let
x
=
ln
t
x=\ln t
x
=
ln
t
and
y
=
e
2
t
y=e^{2t}
y
=
e
2
t
for
t
>
0
t>0
t
>
0
. (i) Obtain
d
2
y
d
x
2
\dfrac{d^{2}y}{dx^{2}}
d
x
2
d
2
y
in terms of
t
t
t
. (ii) Show that
d
2
y
d
x
2
>
0
\dfrac{d^{2}y}{dx^{2}}>0
d
x
2
d
2
y
>
0
for every
t
>
0
t>0
t
>
0
.
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