Finding the Equation of a Tangent Line to a Curve at a Given Point
Problems That You Should Practice
- Calculate the derivative using the power rule.
- Evaluate the derivative for the x value of the given point. The answer to this is the slope.
- Take the slope and the given point. Use them in the point slope formula to calculate the equation of the tangent line.
Directions: Please find the equation of the line that is tangent to the given curve at the given point.
Step 1
Step 2
Therefore, m = 8
Step 3
| Plug into the point slope formula. |  |
| Distribute. | |
| Add 12 to both sides. |
You can check this by graphing the original function on MATLAB or a graphing calculator along with the equation of the line that you just calculated. The line should "skim" the curve at the point (1,12).
Problems that You Should Practice
Directions: Please find the equation of the line that is tangent to the given curve at the given point.
