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

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

15 votes
15 votes

Answer:

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}.

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