QUT MZB127 Eng. Mathematics and Statistics Problem Solving Task A Question 1 This question concerns the flow of water through a parabolic-shaped channel described by y = x2 (x and y in metres). The channel is filled up to a depth h (metres). The cross section is show below: y = x2 yr y = h v (x, y ) A The water velocity through the channel, v(x, y) (in metres/second), is modelled in this assessment using the following function: v (x, y) = (2h - y) (y - 2:2). (a) (5 marks) Find the maximum velocity by doing the following: i) find all the critical points of the function v(x, y), ii) identify the single critical point that is within the cross section area A depicted above (include ing, possibly, on the boundary). iii) show that this critical point is a local maximum using the Hessian determinant test, iv) evaluate the value of v at this maximum