Mathematics

Problem

For

t\ge 0

, consider the function

h(t)=\dfrac{t}{1+t^{2}}

. a. (i) Find the stationary points of

h

in the domain

t\ge 0

." b. (ii) Classify the stationary points obtained in (i)." c. (iii) Hence find the maximum value of

h(t)

for

t\ge 0