# How do you find the local max and min for #F(x) = ln((x^4) + 27)#?

##### 2 Answers

The minimum is

#### Explanation:

Thanks to Jim for pointing out the mistake in the following step that is duly corrected now.

If

F(a) is a local minimum

Here a = 0, n = 3 (odd) and

So, F(o) is local minimum. There is no minimum, elsewhere.. So,

#F(0) = ln 27 = ln (3^3)=3 ln 3 =3.296, nearly, is the minimum of F(x)

**Find the critical numbers:**

The only critical number is

**Test the critical numbers:**

so

(If you prefer, you could use the second derivative test, but in this case the first derivative test is simple enough.)