How to find Gradient at a Point on a Curve

In this video we look at finding the gradient at a point on a curve using the tangent.

[@aplaysroblox6755]

very good explanation with details and method.

[@joeyfredericks6020]

Thank you for posting this video has everything on the topic.

[@thayyibrumy9d913]

Thank you so much man you helped me alot , wish you the best in the future :))

[@mamun7911]

Nice teaching....

[@paulkibedy5460]

How to calculate elliptic curve using geometry,your video explains it very clearly,you are a very good teacher,....

[@rostymaths]

Thank you for your kind words

[@eternityj]

Thank you so much!! Very helpful

[@williambunter3311]

Excellent teaching! I have subscribed happily. Thank you and God bless you.

[@oscarwood9060]

You’re going to carry my results , thank you, you’re a god

[@rostymaths]

Thank you for your kind words

[@ROCKY-pu1zt]

Sir, Many, many thanks. I'm trying to get into Medical school and this helps a lot!

[@bamideleoluwafemi9531]

Thank you so much

[@numbers6246]

This way should be explained by any teacher. Very clear for everyone.

[@maimomirabel2685]

Thank u so much

[@Kate-yl1wc]

so helpful thanks

[@ndodanasibanda764]

Thanks 👍

[@timtucker3223]

Ur a great teacher

[@sqeu8252]

very helpful!

[@steve.o4432]

on the last example for grad at x=2 should the change in y be 3.8 and not 5.8

[@steve.o4432]

@George Ross 😂 hopefully other people will notice the mistake

[@DoctorAmadhila]

I don't understand, how did you get gradient (m)= -4 Because I feel like when x= -3 or/ x= 1 the gradient is just positive 4 regardless to which side you have drawn the tangent. Any input?

[@rostymaths]

As a rule of thumb, if the line is going down, the gradient should be negative. Alternatively, use the 2 coordinates I provided at the end of the video and you’ll get -4. The coordinates were (-3, -1) and (-2, -5). Find the difference in y which is -1-(-5) which is 4. Then do the x which is -3-(-2) which is -1. This will give -4 when you divide them.

[@DoctorAmadhila]

Thank you for clarification!

[@Justmaru5]

I have a question. How do you determine which number is your Y2 or Y1

[@rostymaths]

To be fair, it doesn’t matter which you use. You’ll get the same answer. So long as you choose your first coordinate (x1, y1), stick to it in that order.

[@Justmaru5]

@@rostymaths Thank you so much

[@olufemimichael97]

Please I need you to please help me solve this equation y=x^2-3x-5. Find the gradient at x=4, x=0

[@bitsurfer0101]

What if you are given a gradient (start and ending gradient values) and need to find a curve that will pass through both at a tangent?

[@rostymaths]

Nope. That would just be an average over a period of time.

[@awesometool2417]

So would the answer be 4 or -4

[@JosephineMbiaEkouta]

Good morning please how Do we calculate the gradient at the point where x=0

[@zoltanpetofi2964]

since the gradient equals the value of the derivetive at 0, it will be 2. (the derivetive is 2x+2)

[@jonerasmus9399]

Nice methods . Can we differentiate to find m for another method

[@rostymaths]

We can differentiate indeed. However, not at GCSE level. That would be something you do in further maths or A-Levels

[@jonerasmus9399]

Sir is there there a difference between IGCSE and GCSE . I'm writing IGCSE exam and I bought a book that actually taught differentiation so thats was why i was wondering why you used a different method . I agree that differentiation is more a AS and A level topic but some IGCSE text books teach it hehe ! And I'm not talking about core either . When I mean IGCSE I mean on Higher/Extended . Anyways good content , good vibes .Cheers

[@rostymaths]

@@jonerasmus9399 there is a difference indeed. At GCSE level, we won’t cover differentiation. There are a lot of overlap between IGCSE though. Thanks for checking.

[@00verttt]

Maths finals trmw, am I cooked chat?

[@Bobbyaf]

The first gradient should be 3.8....

[@rostymaths]

Have you checked that properly? There is a mistake with the final gradient where I said the correct answer but wrote something else.

[@shaheerx]

Sure! Drawing a tangent on a curve and finding its gradient involves a few steps: 1. **Select a Point:** Choose a point on the curve where you want to find the tangent. This will be the starting point for your tangent line. 2. **Draw a Line:** Draw a straight line that touches the curve at the chosen point. This is your tangent line. 3. **Find the Gradient:** To find the gradient (slope) of the tangent, you can use the formula: \[ \text{Gradient} = \frac{\text{Change in } y}{\text{Change in } x} \] Calculate the change in \(y\) and \(x\) between two points on the tangent line. The ratio of these changes gives you the gradient. Remember, the tangent represents the slope of the curve at that specific point. If you have a specific curve or point in mind, I can provide more tailored guidance!❤

[@mr.rusty1619]

Why didn’t you simply differentiate the quad to yield dy/dx=2x+2, then plug in x=1 or -3 to produce dy/dx=4 and -4, respectively. This exercise takes half a minute and is precise. SMH

[@osumanuabubakar9557]

The question didn't ask you to differentiate. Specifically, the question asked you to find the gradient at given x coordinates. It requires you to be practical. Thank you

[@The_ATF_]

Because it’s easier to just draw a tangent in this case SMH

[@jackbertholet5122]

If you know the equation of the parabola it is way more practical to just differentiate instead of having to draw a tangent which may introduce error. But I think this video was aimed for middle school students who are not required to know anything about calculus@@osumanuabubakar9557

[@TrueOracle]

GCSE maths doesn't need differentiation

[@zoltanpetofi2964]

this has not much to do with math at all. drawing random lines is everything but math. this is only pure speculation, why you drew exactly this line? because you already knew it has to be 4 from calculus. what if x=0,5? the real mathematic way would have been to show that the gradient of the tangent equals the value of the derivative at the tangent point. since the derivetive is 2x+2, it is pretty easy to come to the real solution of 4 if x=1 and to the other real solution of -4 when x=-3. Moreover what you wrote as two differnt methods of calculating the gradient are the same since x2-x1 is exactly delta x and y2-y1 is delta y. the first method is only the special case for the common understanding of gradient, which is: how much to go vertically if i go 1 horizontally. method 2 is the generic one for any random points.

[@IykeDx]

We all never got to the calculus stage of Maths. The Utube name says #rustymaths

[@sissi9100]

Not everything needs to be complicated + there are tons of other more ‘advanced’ math videos you can check out if you’re not satisfied with this.

[@rostymaths]

Great explanation and excellent method. Unfortunately, this is not appropriate for GCSE students. They have to do it the way I demonstrated it. Your method is what I would normally do 😉