Worked example: Approximation with local linearity | AP Calculus AB | Khan Academy

Finding the equation of a tangent line at a point of a curve by knowing the derivative at that point. Then using that equation to approximate the value of the function at close by x-values.

AP Calculus AB on Khan Academy: Bill Scott uses Khan Academy to teach AP¨_ Calculus at Phillips Academy in Andover, Massachusetts, and heÕs part of the teaching team that helped develop Khan AcademyÕs AP¨_ lessons. Phillips Academy was one of the first schools to teach AP¨_ nearly 60 years ago.

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[axelmoreno]

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[aldolunabueno]

0, 615 is a better approximation using second derivative with Taylor polynomial, but for the exercise is fine. However, you should have indicated.

[enrianwicaksana]

Hello ! I'm a student from Indonesia. I think the right answer is 0.7
I find that f''(1, 9)≈3.7 and we know that f''(2)=3
So we can conclude that f'(x) is increasing from 1.9<x<2
From the approximation with the same way as you did we get that f(1.9)≈0.6
Since we know that the magnitude of the tangent line is increasing so point (1.9, 0.6) is below the f(1.9)
So f(1.9) is slightly greater than 0.6 and from the answer is 0.7

That's just my idea. Please review it !!!

[CossZt]

sin(x) = tan(x) = x

*Waits to be exiled*

[samlawler]

At 2:26, how do you know the slope of the tangent line is 4?

[andylaw]

Something coming up from my mind with a T at the