Mathematics

Problem

Let

p(x)=\dfrac{x}{x^{2}+1}

. Which of the following statements about the local extrema of

p

is true? a)

p

has local minima at

x=\pm 1

. b)

p

has no local extrema on

\mathbb{R}

. c)

p

has a local maximum at

x=1

and a local minimum at

x=-1

. d)

p

has a local minimum at

x=1

and a local maximum at

x=-1