1. **Problem Statement:** We are given a function $d = d(t)$ representing the diameter of a peach in centimeters as a function of time $t$ in days. We need to interpret the derivative $d'(t)$ and compare values at $t=6$ and $t=20$. 2. **Understanding the derivative $d'(t)$:** The derivative $d'(t)$ represents the instantaneous rate of change of the diameter with respect to time. This means it tells us how fast the diameter is changing at any specific day $t$. 3. **Interpretation of $d'(t)$:** - $d'(t)$ is the instantaneous rate of change of the diameter at time $t$. - It can be thought of as the speed at which the peach is growing on day $t$. 4. **Comparing $d'(6)$ and $d'(20)$:** From the graph description, the growth curve is steep near $t=6$ and flattens near $t=20$. This means the rate of growth is faster at $t=6$ and slower at $t=20$. Therefore, $d'(6) > d'(20)$. 5. **Interpretation of $d'(6)$ and $d'(20)$:** - $d'(6)$ is the instantaneous rate of change of the diameter at day 6, representing how quickly the peach is growing on day 6. - $d'(20)$ is the instantaneous rate of change of the diameter at day 20, representing how quickly the peach is growing on day 20. **Final answers:** - (a) $d'(t)$ represents the instantaneous rate of change of the diameter at time $t$. - (b) $d'(6)$ is larger than $d'(20)$. - (c) $d'(6)$ and $d'(20)$ represent the instantaneous growth rates at days 6 and 20 respectively.