Read the following information and answer the two items that follow :

consider the function

$$f(x) = 3{x^4} - 20{x^3} - 12{x^2} + 288x + 1$$

In which one of the following intervals is the function decreasing?

A given quantity of metal is to be case into a half cylinder (i.e. with a rectangular base and semicircular ends). If the total surface area is to be minimum, then the ratio of the height of the half cylinder to the diameter of the semicircular ends is

The minimum distance from the point (4, 2) to y² = 8x is equal to

What is the minimum value of a²x + b²y where xy = c² ?