# How do you find the local extremas for #g(x) = x^2 + 1#?

##### 1 Answer

Jan 8, 2017

#### Answer:

#### Explanation:

We find the critical point as solution of the equation:

As the second derivative is constant and positive this critical point is a local minimum.

The same conclusion can be drawn by direct inspection as:

(i)

#g(x)# is a second order polynomial so it has a single local extreme.

(ii)#x^2>=0# so#g(x) >=1# and#g(0) = 1#