Question

Find the Radius of curvature of the curve y= x3 at (1 1 )

Answer 1

Answer:

Radius of curvature

=∣

y

′′

(1+y

′

)

2

3

∣

Now

y

′

∣

(1,2)

=

y

2x

∣

1,2

=1

And

y

′′

∣

1,2

=

y

2

2y−2xy

′

∣

1,2

=

y

2

2y−2x

y

2x

∣

1,2

=

y

3

2y

2

−4x

2

∣

1,2

=

8

8−4

=

2

1

.

Therefore

R=∣

2

1

(1+1)

2

3

∣

=

2

1

2

2

=4

2