Describe how to determine the average rate of change between x = 2 and x = 4 for the function f(x) = 2x3 + 1. include the average rate of change in your answer.

56

Step-by-step explanation:

The average rate of change is the ratio of the "rise" to the "run" over the interval. The "rise" is the difference between the function values at the ends of the interval:

rise = f(4) -f(2) = (2·4^3 +1) -(2·2^3 +1) = 2(4^3 -2^3) = 2(64 -8) = 112

The "run" is the length of the interval:

run = 4 - 2 = 2

Then the average rate of change for this function is ...

rise/run = 112/2 = 56

4sqrt5

step-by-step explanation:

the base has dimensions of 8 x 4, so the diagonal is 64 + 16 square rooted or 4sqrt5.

the correct answer is 828.07