Question

find the radius of curvature for the curve y=x^3-4x+1 at (-1,2)

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

​

Step-by-step explanation: