For , the critical numbers are . Which of the following correctly ranks the…

MATHEMATICS · Single correct · AP · Calculus AB · Analytical Applications of Differentiation · Analytical Applications of Differentiation

Problem

For g(x)=x4−4x2+1g(x)=x^{4}-4x^{2}+1, the critical numbers are x=−2, 0, 2x=-\sqrt{2},\,0,\,\sqrt{2}. Which of the following correctly ranks the corresponding function values from least to greatest? (a) g(−2)<g(0)<g(2)g(-\sqrt{2})<g(0)<g(\sqrt{2}) (b) g(−2)=g(2)<g(0)g(-\sqrt{2})=g(\sqrt{2})<g(0) (c) g(0)<g(−2)=g(2)g(0)<g(-\sqrt{2})=g(\sqrt{2}) (d) g(2)<g(−2)<g(0)g(\sqrt{2})<g(-\sqrt{2})<g(0)

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