Table of contents
- 0. Functions7h 52m
- Introduction to Functions16m
- Piecewise Functions10m
- Properties of Functions9m
- Common Functions1h 8m
- Transformations5m
- Combining Functions27m
- Exponent rules32m
- Exponential Functions28m
- Logarithmic Functions24m
- Properties of Logarithms34m
- Exponential & Logarithmic Equations35m
- Introduction to Trigonometric Functions38m
- Graphs of Trigonometric Functions44m
- Trigonometric Identities47m
- Inverse Trigonometric Functions48m
- 1. Limits and Continuity2h 2m
- 2. Intro to Derivatives1h 33m
- 3. Techniques of Differentiation3h 18m
- 4. Applications of Derivatives2h 38m
- 5. Graphical Applications of Derivatives6h 2m
- 6. Derivatives of Inverse, Exponential, & Logarithmic Functions2h 37m
- 7. Antiderivatives & Indefinite Integrals1h 26m
- 8. Definite Integrals3h 25m
5. Graphical Applications of Derivatives
Curve Sketching
Problem 3.6.50a
Textbook Question
{Use of Tech} Tree growth Let b represent the base diameter of a conifer 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 = 5.67+0.70b+0.0067b².
a. Graph the height function.
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1
Identify the function that relates height (h) to base diameter (b), which is given as h = 5.67 + 0.70b + 0.0067b².
Determine the range of values for b (base diameter) that you want to use for the graph, ensuring they are realistic for a conifer tree.
Calculate the corresponding height (h) values for each chosen base diameter (b) using the function provided.
Plot the calculated (b, h) points on a coordinate system, where the x-axis represents the base diameter (b) and the y-axis represents the height (h).
Connect the plotted points to visualize the relationship between the base diameter and height of the tree, noting the shape of the graph.
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