If h' is a child's rate of growth in pounds per year, what expression represents the increase in the child's weight (in pounds) between the years 2 and 5?
Would I be correct in thinking that h'(5) - h'(2) is the correct expression?
If h' is a child's rate of growth in pounds per year, what expression represents the increase in the child's weight (in pounds) between the years 2 and 5?
Would I be correct in thinking that h'(5) - h'(2) is the correct expression?
If you want the rate of change of the height of the child between years 5 and 2, it'll be $\displaystyle h(5)-h(2)$.
If you want the average rate of change of the height between those years, you need to divide the above expression by the number of years that have passed: $\displaystyle \frac{h(5)-h(2)}{5-2}$
Now, the expression you have given, $\displaystyle h'(5)-h'(2)$ is just the amount that the rate of change has changed. That is you are measuring the difference between how fast the child is growing at 5 and at 2 years.