For the differentiable function

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

Problem

For the differentiable function gg, the derivative is g′(x)=x3−6xg'(x)=x^{3}-6x. The second derivative is g′′(x)=3x2−6g''(x)=3x^{2}-6. Which of the following correctly classifies the critical points of gg? (a) Relative maximum at x=0x=0; relative minima only at x=6x=\sqrt6. (b) Relative maxima at x=0x=0; relative minima at x=6x=\sqrt6 and x=−6x=-\sqrt6. (c) Relative minima at x=0x=0; relative maxima at x=6x=\sqrt6 and x=−6x=-\sqrt6. (d) Relative maxima at x=0x=0; relative minima at x=2x=\sqrt2 and x=−2x=-\sqrt2.

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