Own work. A small cuboid box has a rectangular base of length 3x cm and width x cm, where x>0. The height is y cm, where y>0. The sum of the length, width and height is 20 cm. [9 marks]
Write down an expression for y in terms of x. [1 mark]

The volume of the box is V cm^3. Find an expression for V in terms of x.

Find dv/dx

Find the value of x for which V is a maximum ​

The table below represents the displacement of a fish from its reef as a function of time: time (hours) x displacement from reef (feet) y 0 4 1 64 2 124 3 184 4 244 part a: what is the y-intercept of the function, and what does this tell you about the fish? (4 points) part b: calculate the average rate of change of the function represented by the table between x = 1 to x = 3 hours, and tell what the average rate represents. (4 points) part c: what would be the domain of the function if the fish continued to swim at this rate until it traveled 724 feet from the reef? (2 points)