Gradient of a Point on a Curve

by Batool Akmal

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    So let's not wait any longer and let's go straight into an example. Here we have a question where you are given a curve c. And curve c has the equation 2x squared - 6x + 4. So it's going to be a quadratic, a curve that we've been dealing with. And it's asking us to find the gradient of the tangent to see at point x equals to 3. Now before we start, let's just see if we can model this. So we can kind of figure out what's actually happening. So we're not quite answering the question yet. We're just going to see if we can think about, what this question is actually asking. So I have here, y = 2x2 - 6x + 4. Just like we've mentioned already is a quadratic. We can solve this. So if we say y equals to 0. We can try to factorize it. And see if we can find the two factors. So those points would be the point of intersection on the x axis. If I try that here x and x. And if we try our two factors, 2 and 2. And if you double check this that gives me 2x squared minus 4, minus 2 to give me minus 6x. And then I've got minus 2 times minus 2 to give me plus 4. So I can factorize it. It's fairly nice equation. From here you can say you got two solutions. So you can say that either 2x - 2 = 0. Or x - 2 = 0. When you solve this, you get x equals to 1 you get x = 2 here. So remember I haven't quite started answering the question yet. I'm just trying to imagine what this actually looks like. And for...

    About the Lecture

    The lecture Gradient of a Point on a Curve by Batool Akmal is from the course Calculus Methods: Differentiation.

    Author of lecture Gradient of a Point on a Curve

     Batool Akmal

    Batool Akmal

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