Question

Which set of x-values identifies all critical points of the function f(x) = (x^2-1)/(x^2-4)

Answer 1

3rd option: {0}

Explanation:

Critical points of a function are where
`f'(x)=0`, therefore:

`f(x)=(x^2-1)/(x^2-4)\\\\f'(x)=((x^2-4)(2x)-(x^2-1)(2x))/((x^2-4)^2)\\ \\f'(x)=-(6x)/((x^2-4)^2)\\\\0=-(6x)/((x^2-4)^2)\\\\0=-6x\\\\x=0`

This means that the set of x-values that identifies all critical points of the function is {0}.