Question

The curvature of the function f(x) = x2 + 2x + 1 at x = 0 is?​

Answer 1

Answer:

0

Step-by-step explanation:

Explanation:

As slope can be calculated using derivative and we can also identify coordinates of point using function, we can use point slope form to get equation of tangent.

At  x

= − 1 , as  f ( x )

= −x 2 − 2 x − 1 ,  f ( − 1 )

= − ( − 1 ) 2 − 2 ( − 1 ) − 1

= − 2 + 2 − 1

= − 1

, hence we need a tangent at point  

( − 1 , − 1 )

.

Further as  

f ( x )

= − x 2 − 2 x − 1 ,  f ' ( x )

= − 2 x − 2

, slope of tangent at  

x = − 1

will be  f ' ( − 1 )

= − 2 ( − 1 ) − 2

= 0

, which means the tangent is parallel to  

x

-axis and is of type  

y = k

. As tangent is desired at  

( − 1 , − 1 )

, the tangent is  

y = − 1 or  y + 1

= 0

.