Given f(x) = x2 + 2x + 9, find the average rate of change of f(x) over each of the following pairs of intervals. (a) [1.9, 2] and [1.99, 2] average rate of change over [1.9, 2] 5.9 Correct: Your answer is correct. average rate of change over [1.99, 2] 5.99 Correct: Your answer is correct. (b) [2, 2.1] and [2, 2.01] average rate of change over [2, 2.1] 6.1 Correct: Your answer is correct. average rate of change over [2, 2.01] 6.01 Correct: Your answer is correct. (c) What do the calculations in parts (a) and (b) suggest the instantaneous rate of change of f(x) at x = 2 might be?

Required average rate of change over the interval [1.9, 2] is 5.9, [1.99, 2] is 5.99, [2, 2.1] is 6.1, [2, 2.01] is 6.01 and the instantaneous change at x=2 is 6.

Step-by-step explanation:

Given function is,

To find the avarage rate of change over given intervals. We know from Lagranges Mean value theorem, the average rate of change of a function F(x) over a interval is, .

(a) On the interval,

(b) On the interval,

(c) Instantaneous rate of change at x=2 is,

Hence the results.

Not sure what your choices are on the drop-down, but these expressions are equivalent to each other and include all solutions (all real numbers).

Edit:

1--Equivalent

2--29

3--Equivalent