Mathematics

Problem

Let

p(x)=\dfrac{x^{3}-3x}{x^{2}+1},\; x\in\mathbb R

. a. (i) Find

p'(x)

and solve

p'(x)=0

to determine the stationary points of

p

. b. (ii) Compute

p''(x)

. c. (iii) Classify each stationary point obtained in part (i) and give its exact coordinates. d. (iv) Discuss, with reasons, whether any of the stationary points found represents the absolute maximum or minimum value of

p

\mathbb R

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