A particle's position in feet at 2' seconds as it moves along the x-axis when time, t 2 0 , is given by s(t) = 3'2 7r+10. When is the particle moving to the left? 0 The particle is moving left from t 2 00 seconds to t = % seconds. 0 The particle is moving left from t = 0 seconds to t = 00 seconds. 0 The particle is moving left from t = % seconds to t = 00 seconds. 0 The particle is moving left trcm t = 0 seconds to t = % seconds. An airplane is flying towards a radar station at a constant height of 6 km above the ground. If the distance s between the airplane and the radar station is decreasing at a rate of 400 km per hour when s = 10 km., what is the horizontal speed of the plane? dt km when s = 10 km Hint: Make sure you are mindful of when distances are increasing or decreasing.Use the graph of y = f (2:) shown below, to determine where the function's derivative is positive, negative, or zero. A) Zero: x = i1; positive: x = (1, a: ); negative: 3: =(-1,1) B) Zero: x = 11; positive: x = {- ac , -1); negative: x = (-1, 1} C) Zero: 3:: = i1; positive: x = (- ac , -1) and (1, x: }; negative: in: = ( 1, 1) D) Zero: x = :1; positive: x = {- ac , -1) and (1, :c ); negative: at = (U, 1} Identify the open intervaf) on which the function is increasing. f[$)=($+2}2{$1) Hint: To differentiate, use the product rule OR expand the function and then differentiate. O f[:.c) increases on [00 , 2) , (U , 00) because 1" (3:) 0 on those intervals. 0 f [2?) increases on [2 , 0) because f' (at) > 0 on those intervals. 0 f[a:) increases on [00 , 2) , (0 , 00) because f (3:) > Don those intervals. Enter your answer into the field. Use the format a/b if entering a fraction. Suppose that a and y are both differentiable functions of t and are related by the equation y = VE. Find - when x = 4, given that # = 3 when x = 4. dy dt