Mathematics

Problem

Let

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

for

t>0

. a. Compute

h'(t)

. Show all algebraic steps in your work. b. Evaluate

h'(t)

t=\sqrt{3}

, giving your answer in simplest exact form. c. Suppose

h(t)

models the concentration (in milligrams per liter) of a substance in a reactor at time

t

hours. Interpret the meaning of the numerical value obtained in part (b) within this context, including appropriate units.