Let f(x)=√x² + 5. After simplifying f'(x) is f'(2) is f"(x) is and f'(2) is Round to 4 decimal places when needed. Round to 4 decimal places when needed.

You are lying on the beach watching a balloon float upward at a rate of 2 meters/sec from a point 50 meters away from you on the beach. Express the distance between you and the balloon as a function of time, t, in seconds since the balloon was released.

- 3 If f(x) 24 (Please use the shortcuts to find the derivative.) + 16√√x, find f'(x).

A person leans over a cliff that is 2000 feet high and throws a rock vertically upward at a speed of 100 ft/sec. When it falls, it barely misses the cliff and falls on the ground at the base of the cliff. The height of the rock (in feet) above the ground t seconds after it was thrown is given by the function f(t) = -16^2 + v0t + s0 where v0 is the initial velocity of the rock and so is the original height of the rock. Therefore f(t)=-16t^2+100t+2000. Determine when the rock will hit the ground at the base of the cliff. What was the maximum height of the rock?