Find the second derivative for each of the following. a . f(x) = 13x4 - 7x3 + 5x2 + 11x + 75 b . f (x) = (x3 + 2x2 + 4)(x4-3) C. f(x) = (4x3 - 7x)? d. 12 = y2 + x2 2 . The distance travelled by an object is given by the equation 20t d(t) = = 1+ x2, t20. a. What is the speed of the object at 1s, 2s, and 3s? b . When does the speed reaches 8 m/s? 3. If a ball is thrown upward with a velocity of 25 m/s from the upper observation deck of the CN tower, 450 m above the ground, then the distance, in meters, of the ball above the ground after t seconds is s(t) = 450 + 25t - 4.9t2, t 2 0. a. When does the ball reach its maximum height? Calculate the maximum height of the ball. C . Use the quadratic formula to find how long it takes for the ball to reach the ground. 2 Find the approximate velocity with which the ball strikes the ground. 4. The position function of a particle is s = ts - 60t , t s 0, where s is measured in meters and t is measured in seconds. Find the acceleration at the instance when the velocity is zero (0). 5. A particle moves according to the equation of motion s = ts - 10t3 + 18t, where s measured in meters and t is measured in seconds. Find the displacement and velocity when the acceleration is zero. 6. The motion of a particle is described by the equation s(t) = 2t3 - 15t2 + 33t + 17, t> 0, where s is in meters and t is in seconds. a. When is the particle at rest? b . When is the particle moving is a positive direction? C. Draw a diagram to illustrate the motion of the particle in the first 10 seconds. d. Find the total distance travelled in the first 10 seconds