Let (h(t)= t t^2+1 ) for (t>0 ).

MATHEMATICS · Multi-part · AP · Calculus AB · Differentiation: Definition and Fundamental Properties · Differentiation: Definition and Fundamental Properties

Problem

Let h(t)=tt2+1h(t)=\dfrac{\sqrt{t}}{t^2+1} for t>0t>0. (1) Compute h′(t)h'(t). Show all algebraic steps in your work. (2) Evaluate h′(t)h'(t) at t=3t=\sqrt{3}, giving your answer in simplest exact form. (3) Suppose h(t)h(t) models the concentration (in milligrams per liter) of a substance in a reactor at time tt hours. Interpret the meaning of the numerical value obtained in part (b) within this context, including appropriate units.

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