# What are the local extrema, if any, of #f (x) =2ln(x^2+3)-x#?

##### 1 Answer

#### Answer:

#### Explanation:

We have:

the function is defined in all of

We can identify the critical points by finding where the first derivative equals zero:

so the critical points are:

Since the denominator is always positive, the sign of

Now we know that a second order polynomial with positive leading coefficient is positive outside the interval comprised between the roots and negative in the interval between the roots, so that:

#f'(x) < 0# for#x in (-oo, 1)# and#x in (3,+oo)#

#f'(x) > 0# for#x in (1,3)#

We have then that

graph{2ln(x^2+3) -x [-1.42, 8.58, -0.08, 4.92]}