Application Of A Mathematical Modelling In Solving Problems

   Using differentiation find the difference between maximum and minimum heights for both the roller coasters.

 1.    The brochure for the Feel the Fear coaster says that the height of the coaster can be determined by this polynomial model for 12 seconds after the coaster comes out of a loop

Find the maximum and minimum heights.

Draw the graph (by hand)   When is the coaster at ground level? Confirm using factor theorem.

2.   The Giant coaster is modeled by

The height of the coaster can be determined for the first 12  seconds of the ride by this polynomial.

Calculate maximum and minimum heights using differentiation then draw the graph(by hand)

Where does the ride start?

The ride has 100 metres of fencing to make a rectangular enclosure as shown. It will use existing walls for two sides of the enclosure, and leave an opening of 2 metres for a gate.

a Show that the area of the enclosure is given by:

   A = 102x – x²

b Find the value of x that will give the maximum possible area.

C  Calculate the maximum possible area

Snacks will be provided in a box with a lid (made by removing squares from each corner of a rectangular piece of card and then folding up the sides)

You have a piece of cardboard that is 40cm by 40 cm – what dimensions would give the maximum volume?