Let $p(x)=x^3 - a x$, where $a$ is constant and $a>0$.

Find the local maxima and minima of $p$.
(Enter your maxima and minima as comma-separated xvalue,classification pairs. For example, if you found that $x = -2$ was a local minimum and $x = 3$ was a local maximum, you should enter (-2,min), (3,max). If there were no maximum, you must drop the parentheses and enter -2,min.)

maxima and minima:

What effect does increasing the value of $a$ have on the $x$-position of the maximum(s) you found? (Enter left, none or right if it moves left, has no effect, or moves right.)

What effect does increasing the value of $a$ have on the $x$-position of the minimum(s) you found? (Enter left, none or right if it moves left, has no effect, or moves right.)

What effect does increasing the value of $a$ have on the $y$-coordinate of the maximum(s) you found? (Enter up, none or down if it moves up, has no effect, or moves down.)

What effect does increasing the value of $a$ have on the $y$-coordinate of the minimum(s) you found? (Enter up, none or down if it moves up, has no effect, or moves down.)