Solve the following questions (Calculus 1)

4. Determine the cubic polynomial in the form f(x) = 1253 + bx2 + cx + d, that contains a yintercept at 2, a horizontal tangent at x = 2 and to which the line y 6 = 3x is tangent at x = 1. 5. The following graph shows the position y = 50:) in metres of an object 43% moving along a straight line at the time t seconds. 4_ 0) Use the graph of the position function to determine the time intervals when the velocity is positive, negative, or zero. b) Sketch the graph of the velocity function. c) Use the graph of the velocity function to determine the time intervals when the acceleration is positive, negative, or zero. d) Is the object speeding up or slowing down at a time of 5.5 seconds? Justify your response. 6. A line through the point (3, 3) forms a right triangle with the xaxis and yaxis in the 1er quadrant. Determine the equation of the line that will (13) minimize the area of the triangle. \"i I I mm 7. Find the value of the constant b such that the function f(x) = Ix + 1 +E has a point of inflection at x = 3