\f\f\fFind the equation of the tangent line. Put answer in slope-intercept form 8. y=_4x2+l2 at(1,3) x 9. Find the second derivative of y = see A? 10. Find all points on the graph of y = x3 -x2 where the tangent line is horizontal. 1 1. Find all points on the graph of y = - x + x - x where the tangent line has a slope of -112. If a ball is dropped from the top of a building that is 400 feet tall, and air resistance is neglected, the heights (in feet) of the ball at time t (in seconds) is given by s(t) = 16t2 + 400. Find the average velocity of the object over the interval [1, 4]. 13. A ball is thrown straight down from the top of a 280 ft building with initial velocity of -12 ft/sec. s(t) = gt2 + 1201+ so Find the position function. What is the velocity after 1 second? What is the velocity after falling 88 feet? What is the velocity at impact? \f15. A particle is moving along a horizontal line and its position at any time t is given by 3 S(t) = t3 t2 6t+ 2 where t is measured in seconds and sis measured in meters. a) Find the velocity and acceleration functions. b) Determine the intervals where the particle is moving to the left. c) Find the average velocity from t = 0 to t = 4? d) Find the instantaneous velocity at t = 3. e) Find the position of the particle the first time the velocity is zero. f) Find the acceleration each time the velocity is 10 m/sec. g) Find the total distance traveled in the first 12 seconds? h) When is the particle slowing down? When is it speeding up? (A particle is slowing down when the velocity and acceleration functions are opposite in sign. A particle is speeding up when the velocity and acceleration are the same sign)