Question

let b represent the base diameter of a certain type of tree and let h represent the height of the tree, where b is measured in centimeters and h is measured in meters. assume the height is related to the base diameter by the function h = 5.43+0.70b + 0.0061b². a. graph the height function. b. plot and interpret the meaning of \\(\frac{db}{dh}\\). interpret the meaning of \\(\frac{db}{dh}\\). choose the correct answer below. a. it is the average growth rate of the base diameter with respect to the height. b. it is the growth rate of the base diameter with respect to the height. c. it is the average growth rate of the height with respect to the base diameter. d. it is the growth rate of the height with respect to the base diameter. b. plot \\(\frac{db}{dh}\\). choose the correct graph below.

Explanation:

Step1: Recall derivative meaning

The derivative $\frac{db}{dh}$ represents the rate of change of $b$ with respect to $h$. Here, $b$ is the base - diameter and $h$ is the height of the tree. So, $\frac{db}{dh}$ is the growth rate of the base - diameter with respect to the height.

Answer:

A. It is the growth rate of the base diameter with respect to the height