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Right now: we're learning about derivatives.

And the questions reads: Determine the coordinates of two points of tangency to the curve y=-2x^2, given that the corresponding tangent lines intersect at (2,8).

What I know:

I know that the derivative of the function is y'= -4x

I know I have to find two equations of lines (equations of the tangent lines). That when I perform the method of elimination (substition, or subtraction), the results will give me 2 for x and 8 for y.

And maybe there's an easier to find it out using derivatives?

But I'm not sure how to start off this question.

The answer in the back of the book is (2+2root2, -24-16root2) and (2-2root2,-24+16root2).

Thank you for the much needed help.

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# Introduction To Calculus Problem (Intersection)

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