Question 1: Let \( h(a)\) represent the median height (in cm ) of a group of people as a function of age \( a \)(in months). Without looking at the data, what do you anticipate the differences in the height functions will be for each sex? Think about the heights of adult men and women and the timing of the puberty growth spurt; be specific. For this problem only consider ages 5 to 20 years, i.e.\(60\leq a \leq 240\). Question 2: Based on your answer to Question 1, sketch two graphs of \( h(a)\) by hand: one for boys, and one for girls. Label both axes of your sketch with the dependent and independent variables, \( h(a)\) and \( a \). Question 3: What does the function \( h^{\prime}(a)\) represent? What are its units? (It may help to know that the limit does not affect units, so the units of the derivative are the same as the units of the secant slope that the derivative is based on.) Question 4: Sketch reasonable graphs of \( h^{\prime}(a)\) for boys and girls that are consistent with your answer to Question 1.