Name: The derivative & tangent line equations | Derivatives introduction | AP Calculus AB | Khan Academy
Uploaded: 2022-07-12T11:56:21.000Z
Duration: 7 min 33 s
Description: Thousands of YouTube videos with English-Chinese subtitles! Now you can learn to understand native speakers, expand your vocabulary, and improve your pronunciation...

- [Voiceover] We're told that the tangent line to the graph

of function at the the point two comma three

passes through the point seven comma six.

You might want to draw it out or just visualize it

draw the information that they are giving us.

Let's see the relevant points here at two comma three

and I'm going to go one, two, three, four,

so that's two comma three and we also have

Seven comma six is going to be right over there.

Let us remind ourselves what they're saying.

They're saying the tangent line to the graph of function f

So if it's the tangent line to the graph at that point,

that's the only place where it intersects our graph

and so the tangent line is going to look like,

So the tangent line is going to look like that.

It goes, it's tangent two f right at two comma three

and it goes through the point seven comma six

and so we don't know anything other than f

so that line has to be tangent to our function

So our function f could look something like that.

They gave us, they gave us the two points that sit

because that is going to be the rate of change of

It's going to be the slope of the tangent line

to go from two comma three to seven comma six,

we go from y equals three to y equals six.

which is the derivative of the function at two

because this is the tangent line at x equals two.

we are given that g of negative one equals three

and g prime of negative one is equal to negative two.

What is the equation of the tangent line to the graph of g

I think it will be helpful to graph this.

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The derivative & tangent line equations | Derivatives introduction | AP Calculus AB | Khan Academy

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