Chapter 12.23, Problem 17MP

Let $\alpha$ be the first positive zero of $J_1(x)$ and let ${\beta }_n$ be the zeros of $J_0(x).$ In terms of $\alpha$ and ${\beta }_n,$ find the values of $x$ at the maximum and minimum points of the function $y=x{J}_1(\alpha x).$ By computer or tables, find the needed zeros and compute the coordinates of the maximum and minimum points on the graph of $y(x)$ for $x$ between 0 and 5. Computer plot $y$ from $x=0$ to 5 and compare your computed maximum and minimum points with what the plot shows.