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Calculus 1: Linear Approximations and Differentials (Video #18) | Math with Professor V

Math with Professor V

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Using the tangent line to a curve as a linear approximation for the function near the point of tangency. Examples finding the linearization of a a function at a certain point. Using differentials to approximate the change in a function, and graphically interpreting the change in f(x) versus the change in y in the tangent line (dy).

AP Calculus AB/BC Unit 4 | Use derivatives for linear approximations and differentials. Directly aligned with Unit 4, tested in both MC and FRQ.

#differentials #linearization #linearapproximation #calculus #calculus1

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20 Comments

@mathwithprofessorv Creator 5 months ago Pinned

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@shaunaugeri8200 3 years ago

You’re the only video that talks about when a=0 you have to make an equation from .95=1+x and then solve for x, and that you can’t just plug in 0 which seems to not be in line with the last part of the equation (x-a). It was a really non-intuitive leap that I didn’t see. It IS annoying that all other problems I tried where a doesn’t equal 0, you can just plug that in fine and get a good answer. Long story short you just lowered my stress levels astronomically ❤

@z.3424 11 months ago

Thank you very much for making this video. I have an exam soon and was feeling really behind. Your way of explaining this whole concept makes me feel much more at ease in understanding.

@JessicaMaharjan-dk6ud 1 year ago

my professor taught me the same topic in class, but I don't understand anything at all. Sometime, lecture video from YT is much better than most of the professor in college.

@amyzhang6016 4 years ago

your explanation made the whole topic much easier. Thank you

@mclovin6537 4 years ago

I searched for linear approximations and am so glad I found your channel, well done.

@MagicStoryWorld123 2 years ago

I'm working on reset exam for calculus. This was so helpful. Thank you so Much. ❤❤

@sanly-cz3hd 3 years ago

wow, your lessons are incredible! you’re getting me through calc😭🙏TYSM

@osobukolakanmi1173 2 years ago

Really helpful video

@Buddhabebop 6 months ago

why towards the end of the use of differentials on e^-0.015 did professor then add e^0 + dy?

@fadiglish6457 4 years ago

Thanks a lot .
Your explanation was really helpful

@marierri 3 years ago

Thank you so much for these videos Prof. V, they are truly super helpful and are giving me ease as I review for my Final. <3

@KM-kh3im 4 years ago

Nice video! You deserve more attention! Please continue with you great work.

@chidubemnwanisobi4999 4 years ago

i honestly love your videos a lot lol.

@aliks4794 5 years ago

Great explanation. Thanks!

@mindyrose64 4 years ago

ECXELLENT explanation

@carrykohli 2 years ago

Thank you for the proper explanation...I wish you were my professor instead of my current one😂

@lachiquitita5412 1 year ago

Hello! I have a question, at 28:38 when you were calculating for the delta y, why didn't we use the delta y = f(x+delta x) - f(x)? I tried using that formula but I got a different delta y, which is 0.01488