Question

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

Answer 1

Answer:

3rd option: {0}

Step-by-step explanation:

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

$f(x)=\frac{x^2-1}{x^2-4}\\\\f'(x)=\frac{(x^2-4)(2x)-(x^2-1)(2x)}{(x^2-4)^2}\\ \\f'(x)=-\frac{6x}{(x^2-4)^2}\\\\0=-\frac{6x}{(x^2-4)^2}\\\\0=-6x\\\\x=0$

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