Question

find the radius of curvature of xe^x when y is minimum?​

Answer 1

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

.