Find the most general antiderivative of the function. (Check your answer by differentiation. Use C for the constant of the antiderivative.) 2t4+6\\/E f(t) = Find a function f such that f'(x) = 3x and the line 81x + y = 0 is tangent to the graph of f. f ( x) =A particle is moving with the given data. Find the position of the particle, 5(t). a(t) = 2t + 3, 5(0) = 6, v(0) = 6 A stone is dropped from the upper observation deck of a tower, 850 m above the ground. (Assume g = 9.8 m/sz.) (a) Find the initial values of the velocity v (in m/s) and the distance 5 (in meters) of the stone above the ground. v(0) = m/s 5(0) = m Find the velocity (in m/s) of the stone at time 1'. Find the distance (in meters) of the stone above ground at time t. (b) How long (in seconds) does it take the stone to reach the ground? (Round your answer to two decimal places.) 5 (c) With what velocity (in m/s) does it strike the ground? (Round your answer to one decimal place.) m/s (d) If the stone is thrown downward with a velocity of 4 m/s, how long (in seconds) does it take to reach the ground? (Round your answer to two decimal places.) 5