3. The tangent lines to the graph of f(x) = x2 grow steeper as x increases. At what rate a the slopes of the tangent lines increase? 6 . 4. Find the second derivative of the function y = 4(3x2 - 5)6 5 . ~ (6x3 + 7 tan x) =1. A particle moving along a line has position s(t) = t - 18t meters at time t seconds. What are the equations as a function of t for the velocity, acceleration and jerk for this particle? At what times does the particle pass through the origin? At which times is the particle instantaneously motionless (zero velocity)? 2. The equation for free fall at the surfaces of two planets (s in meters, t in seconds) are s = 11.55t on Jupiter and s = 5.512 on Neptune. What would have been the rock's velocity, speed, and acceleration at time t on each planet? How long does it take a rock falling from rest to reach a velocity of 125 meters per second on each planet? (Round to the hundredth of a second)