Find all critical numbers for the function f(x) = x - 1 / x + 3.?

Answer 1

x=n is a critical point of f(x) when
either:
f'(n)=0 OR f'(n) does not exist
to find them we must take the first derivative

the first derivative of this function using the quotient rule:
(u'v-uv')/(v^2)
the derivative is
f'(x) = (1)(x+3)-(x-1)(1)/((x+3)^2)
as you can see, if you look at the denomenator
if we have x=-3, then the function becomes 0^2 and since dividing by zero is not allowed, teh derivative does not exist at that value (something like an asymptote)
critical numbers for this function is hence
x = -3 since f'(-3) does not exist.

The other critical numbers are found when f'(n) = 0
in this derivative, there is no value such that it will make it zero, the derivative is never zero hence x = -3 is the only critical value of this derivative

Answer 2

I belive x = 1 is the only critical number in that function since that makes the top half of the equation = to 0.

x = -3 is not a critical number because it would make the function undefined. A critical number makes a function = to 0, not undefined.

Hope this helps

Answer 3

It seems like the numbers 1 and 3 are the critical numbers in that equation.

Answer 4

x= -3 ?

Answer 5

The only one is x=-3 as the derivative is never zero