Hello, I need help with these grade 12 calculus and vector math questions, please. For a good review please be detailed and thorough when answering the questions. And please answer all the questions correctly too :)

Thank you

1. Which of the following is true for the interval (2, co) for the graph of f(x) shown below? a. f'(x) > Of"(x)>0 c. f'(x) 0 b. f'(x) > Of "(x) 5, then which choice is not a possibility for f'(x)? a. f'(x) =x-5 c. f'(x) =-x2+ 10x-25 b. f' (x ) = 5-x d. f'(x) =-5 3. Let the graph below represent a derivative function, f'(x). For which values of x is the * original' function, f(x), increasing? For which values of x does f(x) have a horizontal tangent? 16+ 12 -17 -16+4 Let the quadratic function s(1) = - x2 + 10x + 15 represent the motion of a toy car as it travels near a sensor. a) At what time / will the car's distance from the sensor be the greatest? b) What is its velocity when the car is at that point? c) Is the car moving toward or away from the the sensor at t = 6 seconds? (careful...think it through) 5. An object travelling in a straight line has position defined by s(t) = 2+3 - 12t, t > 0 where s is measured in metres and t in seconds. i. Find the velocity and acceleration of the object at t = 1 seconds. ii. Does the object start from rest at t = 0? Explain. ii. What is its position when the object stops? Describe the subsequent motion of the object. iv. Determine whether the speed of the object is increasing or decreasing at t = 3 seconds. Explain your answer by describing the object's motion at that time.6. Docking gently. With its motor lifted at t = 0, a boat glides towards a dock. Its distance (in metres) from the dock is given by t s(t) = N S 3+t for t > 0, where so is a positive constant. a. Find the boat's velocity v(t) and explain its sign. b. If the driver wishes to reach the dock with a speed of 0.5 metres per second, how far from the dock should the driver lift the motor