Science talk:Math Exam Resources/Courses/MATH100/December 2013/Question 08 (a)
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|Domain of f is x >= 0||2||20:02, 1 November 2014|
This function is only defined for x \geq 0. Same for part (b). In the hint, please add that points where the derivative DNE are also considered critical points. As a consequence, 0 is also a critical point here, since f'(x) \to \infty as x \to 0.
Pardon my ignorance, but why is the function not defined for x < 0? At x = -1, is its value not 77? and . . Please help me to understand if I am overlooking something.
You are absolutely right! This works because of the odd denominator in the fractional power. I was confused because, in general, the n-th root of a negative number has n solutions, if you allow complex numbers. This is also the reason why google & wolframalpha etc tell you that (-1)^(2/7) is a complex number. None of that fanciness is necessary here, and your solution is very clear. Good job.