Finding critical points of an equation

Question

Find the crital numbers from the equation X+2 divided by X-2

Answer 1

(x + 2) / ( x - 2) first we are not allowed to have 0 in the denominator, so if x = 2 we have a critical point at x = 2 because the denominator = 0.  this tells us something is happening at this point.

f(x) = (x+2)/(x-2)

To find the first derivative we need to use the formula vu' - uv'/ v^2.

u = x + 2                                v = x - 2

u' = 1                                     v' = 1

f'(x) = (x-2)(1) - (x+2) (1) / (x+2)^2

f'(x) = x-2 -x -2 / (x+2)^2

f'(x) = -4 / (x+2)^2

set the f'(x) = 0 to find any further critical values.

-4 / (x+2)^2 = 0

no more because we multiply (x+2)^2 by 0.