Determine all critical points for the function.
-$$f ( x ) = \frac { - 6 x } { x + 2 }$$
A) x = -2
B) x = -12 and x = 0
C) x = 2
D) x = 0 and x = -2

Question

Quizplus · Accepted Answer

To find the critical points, we need to find the values of x where the derivative of f(x) (i.e. f'(x)) equals zero or where it is undefined. 
Using the quotient rule of differentiation, we get: 
f'(x) = $\frac{(-6)(x+2) - (-6x)(1)}{(x+2)^2}$ = $\frac{-12}{(x+2)^2}$ 
The derivative is undefined at x = -2 because the denominator becomes zero. 
To see if there are any other critical points, we set the numerator of the derivative equal to zero and solve for x: 
-12 = 0 
There are no real solutions to this equation, so -2 is the only critical point.

Determine All Critical Points for the Function f(x)=−6xx+2f ( x ) = \frac { - 6 x } { x + 2 }f(x)=x+2−6x​

Determine All Critical Points for the Function $f ( x ) = \frac { - 6 x } { x + 2 }$