To find the rate of change of the function h(x) = 2x over the interval from x = 2 to x = 4, we need to calculate the average rate of change of the function on this interval. The average rate of change is given by the formula:
Average Rate of Change = \( \frac{h(b) – h(a)}{b – a} \)
where a and b are the endpoints of the interval.
In this case, a = 2 and b = 4. First, we need to evaluate the function at these points:
- Calculate h(2):
\( h(2) = 2 \times 2 = 4 \) - Calculate h(4):
\( h(4) = 2 \times 4 = 8 \)
Now we can substitute these values into the average rate of change formula:
Average Rate of Change = \( \frac{h(4) – h(2)}{4 – 2} = \frac{8 – 4}{4 – 2} = \frac{4}{2} = 2 \)
So, the average rate of change of the function h(x) = 2x over the interval from 2 to 4 is 2. This means that for every unit increase in x, the function h(x) increases by 2 units.