For the given polynomial function, determine the local behavior at each x-intercept.
f(x) = 2x\textsuperscript{3}(x - 7)\textsuperscript{6}
touches x-axis and turns around at (2, 0); crosses x-axis at (7, 0)
crosses x-axis at(-2, 0); touches x-axis and turns around at (7, 0)
touches x-axis and turns around at (3, 0); crosses x-axis at (-7, 0)
crosses x-axis at (0, 0); touches x-axis and turns around at (7, 0)