Curve sketching
Task
Given is the function .
a) Plot the graph of f(x).
b) Calculate the roots, local extrema and inflection point of f(x).
c) Estimate the arguments x, where the tangent on f(x) has a slope of 30°.
d) Estimate the equation of the tangent on the graph of f(x) in x = 2.
Explore the construction...
Instructions
| 1. | Enter the equation of the function into the Input Bar and press Enter. |
| Note: The graph of f(x) will be displayed in the Graphics View. | |
| 2. | Calculate the roots of f(x) by entering the command or into the Input Bar. |
| 3. | To calculate the local extrema of f(x) use the command . |
| 4. | Check if x = 1 and x = 5 are arguments of minimal or maximal turning points by calculating the second derivative and . |
| 5. | Calculate the y-coordinates of the turning points by entering into the Input Bar. |
Try it yourself...
Instructions (continued)
| 6. | To calculate the inflection points, use the command and choose Add label from the context menu to name the list of solutions l1. As only one of the solutions is in the domain of f(x), enter to label this solution and to be able to reuse it in further calculations. |
| 7. | Calculate the y-coordinate of the inflection point by entering into the Input Bar. You can now display the inflection point by entering its coordinates A=(a, b). |
| 8. | To find the arguments x, where f(x) has a slope of 30°, enter the command . |
| 9. | Estimate the equation of the tangent on f(x) at x = 2 by entering into the Input Bar. The tangent will be displayed in the Graphics View. |