What does the question mean when it says "defined for all real numbers x"?

Question

(No calculator allowed)

What are the critical numbers for the function f(x) that is defined for all real numbers x if:

f'(x) = (x²-16)/(2x²+7x-15)

What does the question mean when it says "defined for all real numbers x"? Does that mean you have to solve it differently than a normal critical numbers problem? Also, if you do have to solve it differently, could someone explain how to? Thank you in advance!

Edit: I tried to solve it and got x = 4, -4, 3/2, -5. Is this correct?

Answer 1

A critical number is a value x = c such that f'(c) = 0 or f'(c) is undefined. If you factor the numerator and denominator of the given derivative you get

f'(x) = 0 when the numerator is zero, and f'(x) is undefined when the denominator is zero.

So your answer is correct.