Let for all real

MATHEMATICS · Subjective · AP · Calculus AB · Analytical Applications of Differentiation · Analytical Applications of Differentiation

Problem

Let

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

for all real

x

. (a) Show that

g

has exactly two critical points. (b) Find the interval(s) on which

g

is increasing and on which it is decreasing. (c) Hence obtain the local maximum and minimum values of

g

and the points at which they occur.