Find the coordinates of the points where the tangents to the curve f(x) = x^3 − 3x − 1 are perpendicular to the line x + 3y = 3. Hence find the equations of the normals at these points.

Question

anonymous · Answer

I know how to do it but it's a non-calculator question and it has surds and so I couldn't really finish it.

anonymous · Answer

Well what is the first step?

anonymous · Answer

what I first did was use the line x + 3y = 3 to find the gradient of the tangent and then the gradient of the normal. then I found the derivative of the equation and found the x-values for the tangent, to be +-Sqrt 8/9

anonymous · Answer

I am not sure if those x values are correct and I get stuck when substituting those x values back into the original equation to find the y values, it's a non-calc question just to remind you.

anonymous · Answer

I meant I found the derivative of the original equation** to be exact.

mertsj · Answer

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