Anti-Derivatives
Worksheet
Determine the function f which satisfies the given condition(s). You may check your answers by determining the derivative. 1) f ’(x) = 3x5 – 4x2+ 1, f (0) = 2 π
1
2) f ’(x) = 2
, f (0) = 6
x +1
3) f ’(x) = 2cos(x) + 5 sin(x), f (0) = 6 4
4) f ’(x) = 2 x -­‐
, f (4) = 1 x
4
5) f ’(x) = +ex, f (1) = 4 x
6) f ’(x)= sec2x +1, f (0) = -­‐3 7) f ”(x) = x2 – x3/2, f ’(0) = 5, f (0) = -­‐1 8) f ”(x) = 2ex -­‐ cos(x), f ’(0) = 0, f (0) = 2 1
9) f ”(x) = 2 , f ’(1) = 0, f (1) = 0 x
10) f’ ’’(x) = sin(x), f ”(0) = 2, f ’(0) = 1, f (0) = 0 A particle moves with the given data. Find the position of the particle. 11) v(t) = 3 t , s(9) = 3 12) a(t) = sin(t )+ cos(t), v(0) = -­‐3, s(0) = 5 13) a(t) = t2 + et, s(0) = 0, s(1) = 1 14) Larry drops a ball from a second story window which is 15 feet above the ground. a. Determine the distance the ball is above the ground at any time t. b. How long does it take the ball to reach the ground? c. With what velocity does the ball strike the ground? d. If the ball is thrown with a velocity of 35 ft/sec, how long does it take to reach the ground?