The pressure distribution on a rectangular steel plate supporting a load is modelled by the function:

Question 3 The pressure distribution on a rectangular steel plate supporting a load is modelled by the function: PM) = m 83m 1f (y 2r (MPa) where x and y are in meters. (3) 03} (C) Calculate the gradient of the pressure function. Hence, determine the rate of change of pressure at the point (D, l) in the direction of u = i 2j. (6 marks) If the dimensions of the plate is not known, determine the location on the plate where the pressure is maximum and calculate this pressure. Show that this pressure is both a local and global maximum. (10 marks) If the plate is l m long by 2 m wide, such that U E x E l, 0 E y S 2, dctcrminc the minimum pressure on the plate. State any theorems used, if any. (16 marks)