Find the average rate of change of the function on the interval specified for real number h. r(t) = 7t3 on [2, 2 + h]

Answer 1

r(t) = 7t^3

r(2) = 7(8) = 56

r(2+h) = 7(2+h)^3 = 7(8+12h+6h^2 + h^3)

= 56 +84h + 42h^2 + 7h^3

r(2+h)-r(2) = 7h^3 + 42h^2 + 84h

[r(2+h)-r(2)]/(2+h)-2) = 7h^2 + 42h + 84