Consider the family of curves f(x)=xⁿ e ^-7x where n is a positive even integer.

(a) Find the roots of f. (That is, solve f(x) = 0.)

(b) Find the x- AND y-coordinate(s) of all critical points and classify each as a local maximum, local

minimum, or neither.

(c) Sketch f, labeling all the points you found above. Note that this question does not ask you to find the infection points (though doing so is certainly good practice).