The water velocity through the channel, v(r, y) (in metres/second), is modelled in this assessment using the following function: v(x, y) = (2h - y)(y - x2). (a) (5 marks) Find the maximum velocity by doing the following: i) find all the critical points of the function v(r, 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 (b) (5 marks) The flow rate of water Q (metres /second) through the channel is defined as the integral Q = v(x, y) da where A is the cross-section depicted in the figure above. For A =1, calculate the flow rate by doing the following: i) describe the fluid region A mathematically, with a as the outer variable and y as the inner variable, ii) set up and evaluate the double integral. If you want, for fun (but no bonus marks) you can try to find the flux for general depth h