MAT133Y1 Lecture 11: chap11s
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MAT133Y1 Full Course Notes
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Solutions to supplementary questions for hp chapter 11: the curve has derivative 3x2. Let (x0; x3 line at this point has slope 3x2: be any point on the curve. 0, so if (1; 0) is on this line, then the line has equation. Since (x0; x3: is also on this line, we must have y = 3x2. 0(2x0 (cid:0) 3) = 0 so we may conclude x0 = 0 or x0 = 3 straight lines are y = 0 and y = 27. 0(x (cid:0) 1), we see the two: (a) the curve y = x2 has derivative 2x, so the tangent line at the point (2; 4) has slope. 4, and therefore the normal line has slope (cid:0) 1. The equation of the normal line is given by. 2 (b) much the same as above, the tangent line at the point (x0; x2: has slope 2x0 and the normal line has slope (cid:0) 1.
