The tangent to the cubic function that is defined by y = x^3 - 6x^2 + 8x at point A(3,-3) intesects the curve at another point, B. Find the coordinates of point B. Illustrate with a sketch. y' = 3x^2 - 12x + 8 y' = 3(3)^2 - 12(3) + 8 y = -1 <-- slope of the line of A This line also has the point B. y = mx + b -3 = -1(3) + b 0 = b Therefore, line equation is y = -1x. So, I equate: -1x = x^3 - 6x^2 + 8x 0 = x^3 - 6x^2 + 9x 0 = x(x^2 - 6x + 9) 0 = x(x-3)(x-3) x = 3, or x = 0. X = 3 we already have, so x = 0 should be point B. I sub back in X = 0 into the main cubic function and I retrieve

At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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The tangent to the cubic function that is defined by y = x^3 - 6x^2 + 8x at point A(3,-3) intesects the curve at another point, B. Find the coordinates of point B. Illustrate with a sketch. y' = 3x^2 - 12x + 8 y' = 3(3)^2 - 12(3) + 8 y = -1 <-- slope of the line of A This line also has the point B. y = mx + b -3 = -1(3) + b 0 = b Therefore, line equation is y = -1x. So, I equate: -1x = x^3 - 6x^2 + 8x 0 = x^3 - 6x^2 + 9x 0 = x(x^2 - 6x + 9) 0 = x(x-3)(x-3) x = 3, or x = 0. X = 3 we already have, so x = 0 should be point B. I sub back in X = 0 into the main cubic function and I retrieve

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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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