Problem

Find the equation of the tangent line to each cur…

02:23

Problem 17 Medium Difficulty

Find the equation of the tangent line to each curve when $x$ has the given value. Verify your answer by graphing both $f(x)$ and the tangent line with a calculator.
$$f(x)=x^{2}+2 x ; x=3$$

Answer

$y=8 x-9$

Related Courses

Calculus 1 / AB

A Graphical Approach to Precalculus with Limits

Chapter 13

Limits, Derivatives, and Definite Integrals

Section 4

Tangent Lines and Derivatives

Discussion

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Video Transcript

to find the equation of our change in line given. So let's note. To find our change in line, we're gonna need our point slope form this equation of red line. We're gonna need our next on our white points and we're giving our x point. So let's find our corresponding. Why appoint where y point is going to be able to apply it at three. So that's going to be three squared, plus two times three. So that's equal to nine plus six. And what is that? What you could to 15? Okay, I know we also need to find our slope. This here is that slope. So let's find have prime of a where a value is executed green that's going to be able to offer backs, which is X squared, plus two X and then we have minus f of a. Well, what is that we left of a? Well, we said that was or a value is three. That's what we have here. So that's 15 and this is all over X minus a, which is three. Okay, and we also need to find a moment here, so that's right out the limits as X approaches to or actually three of the following. Okay, so we can you write this? My factory Argue right up is a factor. Are new maitre into exports five times X minus three over X minus three. Now let's cancel all of our, like terms and unused rectum. So we get it. That's 345 1/5 of this year is our spoke. Okay, so let's put that into our equation. Here we have y minus. Why one I was 15 is equal to eight times X minus three. Now let's move to play out our eight. What is eight times three? That's going to be 24. And then we also want to add 15 on both sides here. Okay, so we get our equation over Lined is why is equal to eight X and then we have negative 24 plus 15. So that's minus nine.

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