find the radius of curvature of xe^x when y is minimum?
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find the radius of curvature of xe^x when y is minimum?
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Answer:
Let y=xe
x
Differentiate both side w.r.t.
′
x
′
⇒
dx
dy
=e
x
+xe
x
=e
x
(1+x)
Put
dx
dy
=0
⇒e
x
(1+x)=0
⇒x=−1
Now,
dx
2
d
2
y
=e
x
+e
x
(1+x)=e
x
(x+2)
(
dx
2
d
2
y
)
(x=−1)
=
e
1
+0>0
Hence, y=xe
x
is minimum function and y
min
=−
e
1
.