How To Find The Equation of The Tangent Line With Derivatives

TL;DR

Learn how to find the equation of a tangent line given a point using derivatives.

Transcript

in this lesson we're going to focus on how to find the equation of a tangent line given a point using derivatives so let's say if we have a function f of x and it's equal to 2x squared minus 5x plus three and we wish to find the equation of the tangent line when x is equal to two so what equation should we use we need to use the point slope form of... Read More

Key Insights

• 💁 The equation of a tangent line can be found using the point-slope form or the slope-intercept form.
• ❣️ To find the y-coordinate, substitute the x-value into the original function.
• 🥡 The slope can be found by taking the derivative of the function and substituting the x-value.
• ☺️ The derivative function gives the slope at any x-value.
• 💁 The equation of the tangent line can be written in either point-slope form or slope-intercept form.
• 🫥 Trigonometric functions can also be used to find the equation of a tangent line.
• 🫥 The concept of using derivatives to find the equation of a tangent line applies to various functions.

Questions & Answers

Q: How do you find the y-coordinate when calculating the equation of a tangent line?

To find the y-coordinate, substitute the x-value into the original function. In this case, f(2) was calculated, resulting in y = 1.

Q: What is the relationship between the derivative and the slope of the tangent line?

The derivative is a function that gives the slope at any x-value. The slope of the tangent line at a specific x-value is obtained by evaluating the derivative function at that x-value.

Q: How can the equation of a tangent line be written in slope-intercept form?

Start with the point-slope form using the point (x1, y1) and slope m, then simplify it to the slope-intercept form by distributing the slope and combining like terms.

Q: Can the same method be used to find the equation of a tangent line for trigonometric functions?

Yes, the same method can be used for trigonometric functions. Calculate the y-coordinate by evaluating the function at the given x-value and find the slope by taking the derivative of the function and substituting the x-value.

Summary & Key Takeaways

• The equation of a tangent line can be found using the point-slope form or the slope-intercept form.

• To find the y-coordinate, plug the x-value into the original function. To find the slope, take the derivative of the function and substitute the x-value.

• The slope can change depending on the x-value, but the derivative function gives the slope at any x-value.

• Plug the values into the point-slope form to obtain the equation of the tangent line.