Gradient of a Curve: Summary

by Batool Akmal

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    00:01 So I hope you’re just as excited about this as I have been.

    00:04 You can actually find the gradient of dy/dx, you can find the equation of the tangent, you can find the equation of the normal if you need it too, and you can find out everything about that one line.

    00:15 It’s the little things, but there’s so much detail in that one equation that you can sketch and algebraically manipulate the equation of the line.

    00:24 So let’s summarize everything that we’ve put together.

    00:27 Firstly, remember the dy/dx, finds the gradient of a curve.

    00:32 So that’s really important.

    00:33 If you ever need to find the gradient of a curve you have to differentiate.

    00:37 It’s not like a straight line where you just do delta y over delta x you have to use differentiation, and that is why we’re learning all these new methods of differentiation.

    00:47 Secondly, the gradient or how to differentiate is if you have a function y is equal to x to the power of N, you bring the power to the front and you decrease the power by 1.

    00:59 So this is one of the methods or the easiest methods of differentiation or how to do dy/dx.

    01:06 We then went over the equation of the straight line.

    01:10 So we discussed y equals to mx plus c.

    01:13 And also the alternate equation that I gave which is y minus y1 equals m [x-x1].

    01:21 Like I said, you can use anyone that you want.

    01:23 However, if you do use y equals to mx plus c, you take your gradient, you take your y, you take your x, you substitute that in, and then you find your c and then you put your c back in.

    01:34 However, if you use the other equation, you can do that all in one go.

    01:38 It’s just a derived equation with the mixture of y equals to mx plus c, plus the equation of the gradient.

    01:47 We then discussed the gradients of perpendicular and parallel lines.

    01:52 So it’s important that you remember this rule.

    01:54 The m1m2, m1 multiplied by m2 equals to minus 1, and you’ll see us apply this rule a little bit more us we do the exercises.

    02:05 So, enough of me talking.

    02:09 Now it’s your turn.

    02:10 So have a go at these questions that we have here.

    02:14 The first two should be fairly straight forward but the last one would be a little bit of a challenge which we can try out together.

    02:22 So good luck with the exercise and I’ll see you in the next lecture.

    About the Lecture

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

    Included Quiz Questions

    1. The gradient
    2. The area under the curve
    3. Where the line intersects the axis
    1. The gradient
    2. Where the line crosses the x-axis
    3. Where the line crosses the y-axis
    1. y - y₁ = m(x - x₁)
    2. y + y₁ = m(x + x₁)
    3. x - x₁ = m(y - y₁)
    4. x + x₁ = m(y + y₁)
    5. x + x₁ = m(y - y₁)
    1. -1/m
    2. m
    3. -m
    4. 1/m
    5. c

    Author of lecture Gradient of a Curve: Summary

     Batool Akmal

    Batool Akmal

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