Calculus 2.2 Derivatives of Polynomials
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- เผยแพร่เมื่อ 7 ก.พ. 2025
- Finding derivatives of polynomials using the power rule, constant multiple rule, sum, difference rules, lots of examples of finding the equation of the tangent to the curve at a specific point and finding the equations of a tangent from a point that is not on the curve to the curve (tricky questions!)
Thank you - 4
I am enjoying your lessons and I will soon watch all of your videos.
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Thank you for explaining this so well, I'm a first year uni student and didn't do calculus in high school, I've been watching your videos since grade 10 so I looked through your videos if you had something to help. Sure enough you do. Always a pleaser to hear you explain things in a manner I can understand. I feel a lot less lost and more capable to continue. Thanks you for our ongoing support!
The entire course is there. Hopefully it will help you catch up on missing pieces ❤️
Thank you! During this 3 week break, I am going to try and get ahead of what my class is learning so I can understand the material more for when my teacher actually teaches the stuff
Good plan as I am sure your teacher is going to have to speed through the material in order to cover the curriculum.
I have a simple question so for the last question can I write " Let the point of tangency be x, 2x^2 + 3 " and solve for x instead of a?
And, second question: there are 2 tangent equations right? at x= 4 and 0 and so at x=0, the tangent equation is y=3? "
There isn't anything wrong with using x and 2x^2 + 3, however to better mathematically present your solution it is best to use a new variable. (You will also do this in several questions in vectors as well)
Yes, there are two tangents, and most often there are more than one as I showed with the point (2, -7).
It is best to say the points of tangency occur WHEN x = 4 and When x = 0 rather than AT x = 0 and x = 4 because if you say x = 0 you are implying (0,0) and (4,0) like an x-intercept
I did solve for the equation of the tangent in the comment below.
@@mshavrotscanadianuniversit6234 Thank you so much for clearing that up. By the way, I love your channel and have recommended it to ALL of my friends. We all appreciate your teaching style and how you make maths easy for us to understand. :)))
@user-jr9qi6so1e Thanks for supporting my channel and bringing your friends along 😊
So glad to have these resources available! I was stuck on the exact question from the end of the video. Thanks for sharing your knowledge
Glad it was helpful! Thanks for watching and please encourage others to subscribe and learn. I’m very close to 2 million views!😊
@@mshavrotscanadianuniversit6234 will do! Congratulations and good luck!
You are a phenomenal teacher
You are very kind … thank you 😊
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Professor Havrot's , thank you for an exceptional video/lecture on the Derivatives of Polynomials in Calculus One. In Mathematics, polynomials are simple to work with because they are differentiable and continuous. Many of your examples are simple to follow and understand, however the final example is problematic. This is an error free video/lecture on TH-cam.
Could you explain how to find the equation of the tangent for the last question I’m having a lot of trouble with it
Okay … we found that the slope is 16 and we know that a point on the line is (2, 3)
Now use y = mx + b to find b
3 = 16(2) + b
b = -29
So the equation of the tangent will be y = 16x -29
Would you say you need to have a sketch to solve the final question? I have a rly hard time imagining how I’d do it without the sketch, since I’d need to realize the points are outside of the sketch
A quick sketch always helps visualize what’s happening and also helps to make sense of the question. Highly recommended. 😊
Miss at 19:26, would it be possible for there to be a 3rd tangent where the point lines up with the other side of the parabola
Also for later on in the question, should we say “let the pointS of tangency” since it’s 2 points?
It wouldn’t be possible to be on the other side without passing through the parabola which therefore would not be a tangent as a tangent can only touch at one point only. If you said let the point of tangency and then discovered that there were two, that’s okay, especially if you hadn’t sketched the graph.
@@mshavrotscanadianuniversit6234 oh I see that makes a lot of sense, thank you miss
Ms. Havrot for the last question to find the equation of the tangent line we just plug in (2, 3) into the x and y values in y = mx+b right?
And solve for m
Hi Ms,
I heard you talking about editing in this section and how you had no time to do it. If you want I would be willing to edit your videos for free, they've helped me so much and honestly it wouldn't be hard especially for things such as mistakes. And as always thank you for the amazing video.
That is so kind of you! Let me think about your kind offer.
Much help!
Miss at 3:39 did u mean to write y prime equals?
Yes, you are correct 😊
Thank you!! So helpful :)))
You're so welcome!
For 22:03 shouldn’t it be 4a^2 - 8a I’m just confused here
No, you have 2a^2 = 4a^2 -8a
So if you bring the 2a^2 to the other side you would have 0= 2a^2 - 8a
Youre a legend
Thank you 😊. Glad you’re enjoying my videos.
thanks
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Thank you 🙌
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I gave my test today, and I'm no sure if I have done great😭
Oh dear! You really need to understand this chapter well.
How did you do?