For the function f, given below, find the antiderivative F that satisfies F(1) = 0. f(x) = x - 4x 3 -5 The antiderivative that satisfies the given condition is F(x) =Given the following velocity function of an object moving along a line, find the position function with the given initial position. V) =4':/T, 5(0)=1 The position function is sft) = :1 Given the following velocity function of an object moving along a line, find the position function with the given initial position. v(t)=9t2+6t1;s(0}=0 The position function is s{t) = Consider the following descriptions of the vertical motion of an object subject only to the acceleration due to gravity. Begin with the acceleration equation a(t) = v'(t) = g, where g = - 9.8 m/s. a. Find the velocity of the object for all relevant times. b. Find the position of the object for all relevant times. c. Find the time when the object reaches its highest point. What is the height? d. Find the time when the object strikes the ground. A softball is popped up vertically (from the ground) with a velocity of 26 m/s. a. v(t) =E). Find the function F that satises the following differential equations and initial conditions. F\"'(x) = 18x, F\"(0) =0, m0) = 1, F(0)=5