Final answer:
The derivative of the function is -6.3t^2 + 141.6t - 777.1. The instantaneous rate of change at t = 9 is -13.
Step-by-step explanation:
To find the derivative of the given function, we need to take the derivative of each term separately. The derivative of -2.1t^3 is -6.3t^2, the derivative of 70.8t^2 is 141.6t, the derivative of -777.1t is -777.1, and the derivative of 2893.6 is 0. Therefore, the derivative of the function is -6.3t^2 + 141.6t - 777.1.
To find the instantaneous rate of change at t = 9, we evaluate the derivative at t = 9. Substituting t = 9 into the derivative function, we have (-6.3(9^2) + 141.6(9) - 777.1) = (-510.3 + 1274.4 - 777.1) = -13.
The instantaneous rate of change at t = 9 is -13.