Final answer:
To find the equation of a tangent line, calculate the slope of the function at a point using the derivative. Then, write the equation of the tangent line using the point-slope form and convert it to the slope-intercept form if needed. This task is facilitated by using calculators such as the TI-83, TI-83+, and TI-84+.
Step-by-step explanation:
Finding the equation of a tangent line is a common task in calculus, which involves calculating the slope of the function at a certain point and writing the equation in the slope-intercept form (y = mx + b).
- Identify the function and the point at which you want to find the tangent line.
- Calculate the derivative of the function to find the slope of the tangent line. For the TI calculators, this can usually be done using the appropriate function in the calculator.
- Use the derivative to find the slope at the specific point by plugging in the value of the point into the derivative. This is the value of 'm' in the equation.
- Calculate the y-coordinate of the tangent line by plugging the x-coordinate into the original function.
- Use the point-slope form to write the equation of the tangent line: y - y1 = m(x - x1), where (x1, y1) is the point of tangency and 'm' is the slope.
- Convert to slope-intercept form if necessary. This process applies when using statistical software, spreadsheets, and calculators such as the TI-83, TI-83+, and TI-84+.
When done by hand, these calculations can be tedious, but with a graphing calculator, you can usually perform these tasks with built-in functions that automate the process.