The tangent line to a curve at a point on the curve can never cross the curve at the point of tangency.?

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The tangent line to a curve at a point on the curve can never cross the curve at the point of tangency.?

Is this true?

2006-10-22 03:44:17 · 4 answers · asked by Olivia 4 in Science & Mathematics ➔ Mathematics

4 answers

By definition a tangent line intersects a curve at 1 point only.
If it crossed the line it would have to touch more than 1 point.
However, it may touch the line again but only after the direction of the slope has changed from what it is at the tangent point.

2006-10-22 03:52:57 · answer #1 · answered by albert 5 · 0⤊ 0⤋

False. Consider the tangent line to y=x^3 at x=0.

2006-10-22 10:46:13 · answer #2 · answered by James L 5 · 1⤊ 0⤋

False if the tangent meets an inflection point

2006-10-22 10:59:21 · answer #3 · answered by Stuart T 3 · 0⤊ 0⤋

yes.........it is tanget not crossing the curve AT this point

but it may cross it at any other point.

2006-10-22 10:52:05 · answer #4 · answered by mozakkera 2 · 0⤊ 1⤋