Well, one problem is that you can't use the slope of the tangent line as the slope of the normal line! They are related: once you find the slope of the tangent line, you can use a simple formula to find the slope of the normal line. Second, I'm not sure I agree with your method of computing the slope of the tangent line. Can't you just use the normal Calc I method? Your method got the wrong answer. (I agree with the book's answer completely, by the way).