Tangent Lines Through Points NOT on the Curve!

Sometimes we're required to find tangent lines to a curve that go through a point that's not on the original curve!
How do we do it?
Simply by realizing that slopes of tangents can be calculated using the derivative, or by using good ol' fashioned rise over run!

[@btsforever7815]

THANK YOU SO SO SO MUCH!!!! I was finally able to solve a hw problem after hours of failed attempts!!

[@blossom7662]

THANK YOU SOOO MUCH!!! I have been struggling to figure out this sort of question for a long time!!! You literally save my score!💖🥰

[@damonyiu4699]

Thank you so much. This video was so clear and very helpful.

[@LarryX508]

Tysm! I have been stuck on this question for a while and this video helped me understand it.

[@xa.l3566]

Thanks , I had a hard time trying to solve this tricky question 😭🙏

[@ayyapureddyraghuram]

thankyou sir very nice technique to solve problems

[@Arturglj]

This is gorgeous 💐

[@eliy5550]

THANKS BRO nice tutorial

[@_tvd]

Does it matter which is y1 and x1?

[@larrychooi9354]

Thanks

[@jocelynhunter9542]

(at 4:03) what if the curve in our question is unfactorable? how would i proceed?

[@gabrialpetersen1926]

Quadratic formula or complete the square.

[@raoryuken4460]

Sonunda ödevimi bitirdim, teşekkürler

[@Kapsyloffer]

Legend.

[@ch1ka8]

what about implicit functions?

[@MelvinAdekanye]

*That 1 dislike is my teacher realizing I'm not going to fail the test anymore.*

[@maxghost1766]

How did you find y prime (y’)

[@EdwardChan.999]

y prime (y') means the Derivative of y ( also written as dy/dx, or d(x^2 + 6)/dx ), and it can be found using Differentiation.
Step 1: The derivative of (x^2 + 6) can be split into the derivative of (x^2) + the derivative of (6).
Step 2: Apply the Power Rule, which states that the derivative of x^n = n x^(n-1).
Therefore, the derivative of (x^2) is (2 x^1), which is just (2x);
(6) can be treated as (6 x^0), so its derivative is (0 6 x^-1) or just (0).
Step 3: Add them together, (2x) + (0) is (2x), therefore the derivative of y is (2x).
I hope the steps are clear enough for you to read :)

[@renee746]

what if the question asks you to determine the equations?

[@sammed473]

Make use of the equation form
y - y_1 = m(x - x_1)
Where (x_1, y_1) is the point of tangency and m is the slope

[@rayhanmaulana1813]

bro made me feel like elon musk

[@yayza7881]

there is nothing worth living for anymore

[@yayza7881]

i cannot do this

[@clueloss196]

@@yayza7881 real

[@chiranjeeviprasad8981]

AWESOME 💯❤💯💯💯

[@johnjosephbagasol3801]

i use the same solution and the i get x€R ;(
btw. thanks for the tutorial!