Find the coordinates of the point(s) on the graph of:

$\displaystyle

y = \frac{1}{3}x^3 + \frac{1}{2}x^2 - 2x + 1

$

where there are horizontal tangents

Find the x coordinate of the point(s) where:

$\displaystyle

f(x) = 2x\sqrt{2-x^2}

$

has vertical tangents