Finding The Tangent Line Equation With Derivatives - Calculus Problems | Summary and Q&A

TL;DR

Learn how to find the equation of a tangent line by finding the slope and plugging in the coordinates of a given point.

Key Insights

• ❣️ The equation of a tangent line can be found by finding the value of y for a given x-coordinate and then finding the slope using the derivative equation.
• 💁 Point-slope form and slope-intercept form can both be used to write the equation of a tangent line.
• 😀 When solving for y in a cubic equation, if factoring is not possible, alternative methods such as graphing or approximation can be used to find the values of y.

Transcript

in this video we're going to talk about how to find the equation of the tangent line so let's say if you're given an equation y is equal to let's say 3 x to the fourth minus five x cubed plus six x plus eight and you wanna find the equation of the tangent line at x equal one now there's two things that you need you need the value of x the value of ... Read More

Questions & Answers

Q: How do you find the value of y for a given equation and x-coordinate?

To find the value of y, plug in the x-coordinate into the given equation and solve for y. This will give you the coordinates of the point on the curve.

Q: How do you find the slope of the tangent line?

To find the slope of the tangent line, plug in the x-coordinate into the derivative equation and solve for the derivative at that point. This will give you the slope of the tangent line.

Q: What are the two forms of writing the equation of a tangent line?

The two forms are point-slope form (y - y1 = m(x - x1)) and slope-intercept form (y = mx + b). Both forms can be used to write the equation of a tangent line.

Q: How can you solve for y in a cubic equation without factoring it?

If factoring is not possible, you can use different methods such as using a graphing calculator to find the x-intercepts or plugging in different values for y until you obtain the desired result. These methods help approximate the value of y.

Summary & Key Takeaways

• The video discusses how to find the equation of a tangent line by using a given equation and a specific point.

• The process involves finding the value of y by plugging in the x-coordinate, finding the slope by plugging in the x-value into the derivative equation, and using the point-slope or slope-intercept form to write the equation.

• Two examples are provided to demonstrate the steps involved in finding the equation of a tangent line.