This question concerns the mv of water through a parabolic-shaped channel described by y = I2 {s and y in metres}. The channel is Iilled up to a depth h. [metres]. The cross section is show below: illzr. y} The water velocity through the channel. r:-[s. y} {in metresj'second}. is modelled in this assessment using the following function: \"{3- HJ = [2!!- - ylly - $2]- {a} {5 marks} Find the maximum velocity bv doing the following: i} nd all the critical points of the function v{..r._ 3;}. ii} identify the single critical point that is within the cross section area A depicted abm'e {includ 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 ow rate of water If} {metresfsecond} through the channel is defined as the integral 62 = [L Honda where A is the cross-section depicted in the figure above. For it = l, caJoulate the ow rate by doing the following: i} describe the uid region A mathematically. with .r 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 limb: for general depth h