NOTE: PROBLEM REQUIRES USE OF MAPLE SOFTWARE. YOU MUST PROVIDE COMMANDS HERE (DO NOT PROVIDE OUTPUT)

Consider the curves y=2x^2, y=4x

Find the points of intersection of the curves.

Find the area of the region enclosed by the curves.

Find the coordinates of the center of mass of a thin lamina of uniform density occupying the region enclosed by the curves.

Find the volume of the solid generated revolving the region enclosed by the curves about the x-axis.

Consider the function f (x) = 3x^4 4x^3 12x^2 +5

Find the intercepts of the graph of the function. Approximate irrational values to eight

decimal places.

Find the intervals of increase and decrease, and the relative extreme values of the function.

Find the intervals of concavity and inflection points of the graph of the function.

Plot the graph of the function selecting intervals for x and y over which the features found in problems 5-7 are clearly displayed.