Calculus Problem - Explained with BASIC MATH!

How to find the slope of a tangent line using the first derivative in Calculus. Learn more math at TCMathAcademy.....
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[@lukewalker1051]

70 y.o. retired mechancal engineer who took a lot of calculus 50 years ago. Still remember some of it and this was easy. I always try to perform your problems by your thumbnail in my head with high success rate but once in a while I need some paper or do it on a word doc. Thanks for what you do. My college professors aside from my parents were perhaps the most influential people in my life and so fortunate as no doubt many are gone now.

[@richardhole8429]

In college, 1968,Calc 1, differential calculus was the most fun course I ever took. It came back right away.

[@madman27985]

Which books /authors are good for calculus as per your experience?

[@maureenjacobs3697]

While I am not in school or taking a maths course, I am pleased to see these pop in and it of my suggestions. Practicing keeps me sharp!

[@redblack8414]

I have been following you, John for some time now. Your explanations are the best math explanations that I have seen on YT. 👍

[@chrisdissanayake6979]

d) 1/2 Rise/Run Y= X^2 Y = 2^2 = 4 Y/X = 4/2 = 2. ? ------- I tried, I was wrong. Oh! I had forgotten my basic Calculus! Mr John did a wonderful job teaching me that the slope of the curve is the first derivative of the curve. The formula of the curve is Y = X^2 The first derivative is Y’ = 2X Therefore, as X = 2, the slope = 2X = 2.2 =4

[@erembald2927]

slope = dy/dx = 2x. When x = 2, 2x = 4, slope is 4

[@stephena1196]

You did do a pretty good job.

[@muhammaddikko8006]

Your video is so informative. You help me understand the confusing part of machine learning as a beginner😊

[@mathswithoutwords]

really good video

[@Kleermaker1000]

Differentiation. So y' = 2X and X = 2, so the answer is: the slope (or m) = 4.

[@tomtke7351]

2x is derivative of x^2 At x = 2 2×2=4. Slope = 4

[@mr.mxyzptlks8391]

The answer is 4, based on calculus. Nice vid, but, I don’t feel I like the ‘barely, barely’ touching phrase is precise enough. It is touching, in exactly 1 (0 dimensional) point - see definition of a tangent. Precision in spoken language is important in math. My math teacher confused me once in 7th grade by saying ‘a prime number is not divisible by any other number’. He left out the ‘by 1, or itself’ and that the result is to be another integer! He had implicit assumptions that were, I have to assume, inadvertently projected onto the students. Anyways, while these vids are long, I appreciate the detail and logic paths.

[@panlomito]

f(x) = x² so the first derivative f'(x) = 2x Now x = 2 so f'(2) = 2.(2) = 4 so answer A 🤪 But we are not done yet because there is this line. So I feel the need to find the equation of this line too. Formal equation of a line is s(x) = ax + b and since we found the slope a = f'(2) = 4 so s(x) = 4x +b Now to find b we have to look for the intersection of the slope line with the y-axis or x = 0 We know one point of the line: f(2) = (2)² = 4 so (2 , 4) and we know the slope a = 4 2 steps to x = 0 will give y = 4 - 2.4 = -4 So the intersection with the y-axis is on (0,-4) and b = -4 And now we have the full equation of the slope line s(x) = 4x - 4 Checking s(2) = 4.(2) - 4 = 8 - 4 = 4 is f(2) = 4

[@waynestanley01]

What a coincidence Just last week a coworker was explaining something to me about slopes. I already knew rise over run. When he mentioned derivatives I had to tell him i never studied calculus. Now i understand what he was talking about.

[@chrissullivan40]

Which is the slope is obvious. What is the slope is the problem.

[@erniemorris9991]

😂😂😅

[@lukewalker1051]

slope = dy/dx =2x

[@Darisiabgal7573]

More like what is the 2, the horizontal or vertical displacement. Maybe at some point this math dude will use standard cartographical conventions like the rest of the world. There’s a reason we enumerate the x-axis under that axis tick marks. This goes hand in hand with the problem yesterday when he failed to define his rotation.

[@robertstuart6645]

Might be good sometime in another session to bring in the limit concept to illustrate why the slope of y=x^2 at f(2) is 4.

[@russelllomando8460]

great explanation. Y=MX+B was causing me difficulties. thanks for the fum.

[@Astrobrant2]

Yep. I did the same thing. Then I realized it had to be some other method. I forgot all about the derivative. Well, it's been 57 years.

[@AD-mw5mv]

what whiteboard software is being used?

[@warblerab2955]

So how would you find the slope if the equation was something like y=x^2 + 4 ?

[@MrSummitville]

I think, the " +4 " is irrelevant.

[@memovilmx6239]

​@@MrSummitvillederivative of a constant=0. Because there's no change so no slope. Y is always the same. The slope is the ratio of change between Y and X. An slope of 1 (45°) means that between two points. The difference between the Ys is exactly the same that between the Xs

[@lasentinal]

there might be a problem with the diagram. The point of intersection does not look like it is where x=2 It looks like it is a little less than where x=2.

[@MrSummitville]

The slope is ... UP ! 😂

[@LuisPena-ge2en]

4

[@mahamunibalakrishnan8263]

2

[@kenesufernandez1281]

💖

[@SarahThor-ht4qy]

Dear TabletMath Class; God would like you to know that the slop is 4! Given the formula for a slop is y=x to the second power, and on the x axis is a two, and God would like you to know that I would solve for y by substituting a two, raised to the power of two, which is equaled to four! In the name of Jesus Christ, Amen! Sincerely, God and Sarah Thor-ht4qy