An object is fired upward into the air from a platform. The object's height above the ground is modeled by: h (t) = -5(t)^2 + 50t + 1. where "h" is the height in meters, and "t" is the time in seconds since the object was launched.

a) In the range of 3 and 3.1 seconds, determine the average velocity. To put it another way, figure out the average rate of change in height between 3 and 3.1 seconds.

b) Calculate, to the nearest two decimal places, the object's instantaneous velocity, or to put it in another way, the object's instantaneous rate of change in height, 3 seconds after launch.

c) Draw a graph to visually represent the problem. Determine the vertex of your function, calculate the IROC at this point and explain its significance.