Answer 4, 5 and 6

4. A test rocket meant for orbit is fired straight from a launch pad. Something goes wrong and the rocket comes back down. The height above the ground is modeled by h =$12 - -1', 120, where h is measured in metres and t, in seconds. i. Find the maximum height of the rocket. ii. At what velocity does the rocket hit the ground? iii. When is the rocket speeding up? 6 5. A rectangle PQRS is inscribed in the region between the x-axis and the part of the graph of y = cos 4x in the domain - - Ex - . Determine the coordinates of P for which the perimeter is PQRS is a maximum, R 6. The line y = mx + b intersects the parabola x* = 4py at the points A and B. Find the coordinates of a point P on the arc AOB so that the triangle PAB has a maximum area. B A P O