Consider a group of penguins migrating along a straight coastline. The position of a penguin at time t is given by the function d(t) = 2t2-3t+ 10, where d is measured in meters and t is measured in minutes. (a) Find the average speed of the penguin group over the time interval [1,4] minutes. (b) Prove that there exists a time c in the interval (1,4) such that the instantaneous speed of the penguins at time c is equal to the average speed found in part (a).