Solve the following question (Calculus)

5. The following graph shows the position y = s(t) in metres of an object 4.5 moving along a straight line at the time t seconds. a) Use the graph of the position function to determine the time 3.5 intervals when the velocity is positive, negative, or zero. 3 2.5 b) Sketch the graph of the velocity function. s(t) 2 c) Use the graph of the velocity function to determine the time 1.5 intervals when the acceleration is positive, negative, or zero. 1 0.5 d) Is the object speeding up or slowing down at a time of 5.5 seconds? Justify your response. 5 6 7 8 9 10 * 6. A line through the point (3, 3) forms a right triangle with the x-axis and y-axis in the 1" quadrant. Determine the equation of the line that will (3, 3) minimize the area of the triangle. Minimize This Area 7. Find the value of the constant b such that the function f (x) = Vx + 1+" has a point of inflection at x = 3. 8. Suppose that f(x) and g(x) are positive functions (i.e functions where f (x) > 0 and g(x) > 0) such that f (x) has a local maximum and g(x) has a local minimum at x = c. Show that the function h(x) = has a local g ( x ) maximum at x = c. 9. If y = 2e3x + 5ex, show that y" - 7y' + 12y = 0. 10. The trough in the figure is to be made to the dimensions shown. Only the angle 0 can be varied. What value of 0 will maximize the trough's volume