Chapter 3.CR, Problem 66CR

66. The table shows the recommended dosage of Children’s TYLENOL Suspension Liquid with respect to weight. Let $D\left(x\right)$ represent the dosage (in tsp) for a child weighing $x$ pounds.

$\begin{array}{cc}\begin{array}{l}x,\text{Weight}\text{in}\\ \text{pounds}\end{array}& \begin{array}{l}D\left(x\right),\text{Dosage}\text{in}\\ \text{teaspoons}\end{array}\\ 24\le x<36& 1\\ 36\le x<48& 1.5\\ 48\le x<60& 2\\ 60\le x<72& 2.5\\ 72\le x<95& 3\end{array}$

a. Draw a graph of this function.

b. Find $\underset{x\to {48}^{-}}{\lim }D\left(x\right)$.

c. Find $\underset{x\to {48}^{+}}{\lim }D\left(x\right)$.

d. Find $\underset{x\to 48}{\lim }D\left(x\right)$.

e. Find the dosage for a child who weighs $48$ pounds, $D\left(48\right)$.

f. Is this function continuous for children who weigh between $24$ and $95$ pounds? If not, what are the weighs at which the function is discontinuous.