Question

Find all relative extrema of the function F(X)=16/(X^2+1). Use the Second-Derivative Test when applicable.
Answer
a.
The relative maximum is .1,0
b.
The relative minimum is .0,1
c.
The relative maximum is .0,16
d.
The relative minimum is .0,16
e.
The relative maximum is .16,0

Answer 1

Take the derivative of this function first

Answer 2

here we go

Answer 3

First

set f'(x) = 0
then solve for x, those will give you your critical points

Answer 4

I got 0

Answer 5

-32

Answer 6

also make sure to check the domain of f'(x)
and the domain of f(x)
if something is not in the domain of f'(x) but is in the domain of f(x) then it is a critical point

if a point is not in the domain of f(x) but is in the domain of f'(x) then it is not a critical point

Answer 7

so it is going to be e then

Answer 8

ok make a table