How do you find the local max and min for #F(x) = ln((x^4) + 27)#?
The minimum is
Thanks to Jim for pointing out the mistake in the following step that is duly corrected now.
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:
(If you prefer, you could use the second derivative test, but in this case the first derivative test is simple enough.)