Question

If the function, f(x) = -2x + 6x - 2,

represents the movement of a whale in meters. What is the average rate of change of the whale for x = 2 second and
x = 4 seconds? Label your answer.

Answer 1

Explanation:

To find the average rate of change of the whale's movement between x = 2 seconds and x = 4 seconds, we need to calculate the difference in the whale's position at these two points and divide it by the difference in time.

First, let's find the whale's position at x = 2 seconds:

f(2) = -2(2) + 6(2) - 2 = -4 + 12 - 2 = 6 meters

Next, let's find the whale's position at x = 4 seconds:

f(4) = -2(4) + 6(4) - 2 = -8 + 24 - 2 = 14 meters

Now we can calculate the average rate of change:

Average Rate of Change = (Change in position)/(Change in time)

= (14 - 6)/(4 - 2)

= 8/2

= 4 meters per second

Therefore, the average rate of change of the whale's movement between x = 2 seconds and x = 4 seconds is 4 meters per second.