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    Find the gradients of the curve y= 2x^2 at the points C and D where the curve meets the line y=x+3.

    I have no idea what I am meant to do with this so any help is greatly appreciated thanks

    (Original post by Sukjeetsandhu)
    Find the gradients of the curve y= 2x^2 at the points C and D where the curve meets the line y=x+3.

    I have no idea what I am meant to do with this so any help is greatly appreciated thanks
    It's asking you to find the gradient of where the curve intersects the line  y = x+3

    So first, solve simultaneously and find the point of intersection (the x value, then differentiate and substitute the value of the gradient.

    First solve the two equations simultaneously to find the x coordinates of the points C and D. The differentiate and substitute your value for x in to find out the gradients

    So firstly we need to find the coordinates of the two intersection points by solving a system of two equations (y = 2x^2 and y = x+3).

    To get a general expression for the gradient of the quadratic curve we need to differentiate it with respect to x, which gives you dy/dx = 4x

    Finally plug in the values of the two points you found and you will get the gradients at those intersections.

    Hope it helps

    It helps to make a rough sketch of the graph. In this case, you can see that there will be two points of intersection between y=x+3 and y=2x^2.

    We need to find the gradients of the curve f(x)=2x^2. Remember for a function f(x)=ax^n, where a is a constant, the gradient function is given by f'(x)=anx^{n-1}. Note that this is a gradient function which gives you the gradient of f(x) only at a certain x coordinate.

    So once you calculate your gradient function, we need to find the two values of x to put into our gradient function. The question asks us to find the gradient at the points where the two graphs meet. How can we find these points, you ask?

    Solving simultaneous equations! Note that we only need the x coordinates though. So find the solutions x_1 and x_2 to the simultaneous equations:


    And to find the gradients asked for in the question, simply calculate f'(x_1) and f'(x_2).

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