Name: Derivative as slope of curve | Derivatives introduction | AP Calculus AB | Khan Academy
Uploaded: 2022-07-12T11:56:21.000Z
Duration: 6 min 10 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] What I wanna do in this video

is a few examples that test our intuition

or the slope of a tangent line of a curve

depending on how you actually want to think about it.

this is another way of saying well what's the derivative

let's estimate the derivative of our function at five.

And when we say F prime of five this is the slope

the point five comma F of five right over here

and so if we want to estimate the slope of the tangent line

if we want to estimate the steepness of this curve

So if I were to draw a line starting there

it looks like it would do something like that.

now what makes this an interesting thing in non-linear

the steepness it's very low here and it gets steeper

and steeper and steeper as we move to the right

when X is equal to five remember F prime of five

this would be the slope of this line here.

for every time we move one in the X direction

Delta Y is equal to two when delta X is equal to one.

is going to be equal to two over one, or two.

And it's almost estimated, but all of these are way off.

would mean that as we increase our X our Y is decreasing.

So if our curve looks something like this

that would be very flat something down here

we might have a slope closer to point one.

Negative point one that might be closer on this side

now we're sloping but very close to flat.

A slope of zero, that would be right over here at the bottom

where right at that moment as we change X

the slope of the tangent line right at that bottom point

So I feel really good about that response.

So alright, so they're telling us to compare

the derivative of G at four to the derivative of G at six

if we were to make a line that indicates the slope there

So now that wouldn't, that doesn't do a good job

not shallow's not the word, that's too flat.

the rate of change of Y with respect to X

or that line you can view it as a tangent line

so we could think about what its slope is going to be

Subtitles ListPlay Video

Derivative as slope of curve | Derivatives introduction | AP Calculus AB | Khan Academy

constantly

figure

positive

negative