Question

Find the average rate of change of p(x) = 6x + 4 on the interval [2, 2+ h].

A. 6
B. h
C. (6h + 4)/h
D. (6h + 4)/(2 + h)

Answer 1

The average rate of change of p(x) = 6x + 4 on the interval [2, 2+h] is (6h + 4)/h.

Step-by-step explanation:

The average rate of change of a function is determined by finding the difference in the function values over a given interval and dividing it by the difference in the input values over that interval.
In this case, the function is p(x) = 6x + 4 and the interval is [2, 2+h].
To find the average rate of change, we need to calculate the difference in function values and the difference in input values.

First, we substitute x = 2+h into the function to get p(2+h) = 6(2+h) + 4.

Next, we substitute x = 2 into the function to get p(2) = 6(2) + 4.

Then, we subtract the function values: p(2+h) - p(2) = (6(2+h) + 4) - (6(2) + 4).

Finally, we subtract the input values: (2+h) - 2 = h.

Therefore, the average rate of change of p(x) = 6x + 4 on the interval [2, 2+h] is given by (p(2+h) - p(2))/h = ((6(2+h) + 4) - (6(2) + 4))/h = (6h + 4)/h.

So, the answer is C. (6h + 4)/h.