(10 points) Suppose the location of an object x on a number line (where positive values are on the right) is given by x(t) = t3 6t2 15t (a) What is the velocity of the object at time t? (b) What is the velocity of the object at 1 second? (c) At 1 second, is the object moving to the left or to the right? How do you know? (d) What is the acceleration of the object at time t? (e) At what two times is the object not moving neither left nor right? How do you know? (f) At what time is the object moving the fastest to the left? How do you know? Hint: Look for the vertex of the parabola which is described by the parabolic velocity curve.