Answer to Question #289721 in Calculus for Robin

Question

a. When we cough, the trachea (windpipe) contracts to increase the velocity of the air going out. This raises the questions of how much it should contract to maximize the velocity and whether it really contracts that much when we cough.

Under reasonable assumptions about the elasticity of the tracheal wall and about how the air near the wall is slowed by friction, the average flow velocity y can be modeled by the equation , , where is the rest radius of the trachea in centimeters and is a positive constant whose value depends in part on the length of the trachea. Show that is greatest when that is, when the trachea is about contracted. The remarkable fact is that ray photographs confirm that the trachea contracts about this much during a cough.

b. Take to be and to be and graph over the interval . Compare what you see with the claim that is at a maximum.

this question needs to be done pn matlab. Can anybody do this entire question on matlab and send the graph and graph codes