19.
Let \( f \) and \( g \) be the functions defined by \( f(x) = -\frac{1}{2}x^3 + 3x + 1 \) and \( g(x) = e^{\frac{x}{2}} \).
Let \( h \) be the vertical distance between the graphs of \( f \) and \( g \) for \( 0 \leq x \leq 2 \).
Find the rate at which \( h \) changes with respect to \( x \) when \( x = 1.5 \).
