1.Identify the open intervals on which the function isincreasing or decreasing. (Enter your answers using intervalnotation.) f(x) = sin(x) + 5 0 < x < 2Ï€ increasingdecreasing

2. Identify the open intervals on which the function isincreasing or decreasing. (Enter your answers using intervalnotation.) f(x) = x + 2 cos(x), 0 < x < 2Ï€ increasingdecreasing

3. Consider the following function. f(x) = x + 1 x2 (a) Find thecritical numbers of f. (Enter your answers as a comma-separatedlist.) x = (b) Find the open intervals on which the function isincreasing or decreasing. (Enter your answers using intervalnotation. If an answer does not exist, enter DNE.) increasingdecreasing (c) Apply the First Derivative Test to identify therelative extremum. (If an answer does not exist, enter DNE.)relative maximum (x, y) = relative minimum (x, y) =

4. s(t) = t3 − 5t2 + 3t − 290 (a) Find the velocity functionv(t) of the particle at any time t ≥ 0. v(t) = (b) Identify thetime interval(s) on which the particle is moving in a positivedirection. (Enter your answer using interval notation.) (c)Identify the time interval(s) on which the particle is moving in anegative direction. (Enter your answer using interval notation.)(d) Identify the time(s) at which the particle changes direction.(Enter your answers as a comma-separated list.) t =

5. An air traffic controller spots two airplanes at the samealtitude converging to a point as they fly at right angles to eachother. One airplane is 75 miles from the point and has a speed of450 miles per hour. The other is 100 miles from the point and has aspeed of 600 miles per hour. (a) At what rate is the distancebetween the planes changing?-------- mph (b) How much time does thecontroller have to get one of the airplanes on a different flightpath? -------h

6. An airplane flies at an altitude of y = 5 miles toward apoint directly over an observer (see figure). The speed of theplane is 600 miles per hour. Find the rates (in radians per hour)at which the angle of elevation θ is changing when the angle is θ =30°, θ = 60°,and θ = 80°. (a) θ = 30° rad/hr (b) θ = 60° rad/hr (c)θ = 80° (Round your answer to two decimal places.) rad/hr

7. The formula for the volume of a cone is given below. Find therate of change of the volume for each of the radii given below ifdr/dt is 8 inches per minute and h = 18r. V = (1/3)πr2h (a) r = 9in V' = π in3/min (b) r = 30 in V' = π in3/min