Find equations of both lines that are tangent to the curve y = x 3 3x
Question:
Find equations of both lines that are tangent to the curve y = x3 − 3x2 + 3x − 3 and are parallel to the line 3x − y − 15.
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The slope of the line 3x y 15 or y 3x 15 is 3 so the slope of both tangent lines to the curve is 3 y x 3 3x 2 3x 3 y 3x 2 6x 3 3x 2 2x 1 3x 1 2 Thus 3x 12 3 x 1 2 1 x 1 1 x 0 or 2 which are the xcoordinates at which the tangent lines have slope 3 The points on the curve are 0 3 and 2 1 so the tangent line ...View the full answer
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