Given a cube with sides x inches, let x(t} = t + 2. What is the instantaneous rate of change of the volume, with respect to time, of the cube at t = 1 second? Assume a spring is oscillating and the length of the spring can be described as L ( t ) = = sin (") What is the formula for the instantaneous rate of change of L(t)?Assume a spring is oscillating and the length of the spring can be described as 5mm . What is the formula for the instantaneous rate of change of Lit)? Liti= t A sphere is expanding with time. Assume that the volume of the sphere is v =g, r(t] = t3 + 2. What is the formula for the rate of change of the volume of the balloon, with respect to time? A square with side x, is changing with time where Kit) =3t + 1. What is the formula for the rate of change of the area of the square? A square with side x cm, is changing with time where x(t) = 3t + 1. What is the rate of change of the area of the square when t = 2 seconds?A triangle with constant base b and height h is changing with time where h(t) = 3t + 1. What is the rate of change of the area of the triangle when t = 1?What function should be used to maximize the volume of an open box whose surface area is equal to 20 where the box has a square bottom? What function should be used to minimize the distance between, y = 3x2, and the point (0, 2)? \fA What value of x maximizes the volume of an open box with a square bottom, where the surface area of the box is equal to 20? Sue has enough paint to paint an area 16 square inches . What are the dimensions of the largest closed box (largest volume} that she can paint? Assume that the base of the box is square. An object is traveling along a path described by y: {x + 3 . Where along that path will the object be the closest to the point {2, 0)