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Slide Rule has done an excellent thing here. He's offered 2 correct solutions to this problem. His first solution follows the syllabus and is quite ghastly. His second solution uses l'Hospital's Rule and is outside the syllabus, but is much much nicer. This is an excellent demonstration of...

What the syllabus doesn't tell you is that the second and third derivative tests can be generalised: Successive derivative test: If f⁽ⁿ⁾(x₀)=0 for n=2,3,4,...,2k and if f^(2k+1)(x₀) exists and ≠0 then (x₀, f(x₀)) is an...