implicit derivatives
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The curve (C) is described by the following equation;
(x^2+y^2)^2=k^2*(x^2-y^2), k>0;
a) Find the slope of the tangent of (C) at point P (x0, y0), y0≠ 0;
b) Identify the points of (C) where the tangent is parallel to x-axis.
How to make it in Matlab?I have no idea
回答（1 个）
Walter Roberson
2012-1-30
0 个投票
The slope of the tangent of C at a point is the same as the derivative at that point.
If you solve for y in terms of x and k, then you can take derivatives.
However, you will find that there are 4 solutions, and you will probably run in to imaginary numbers in at least 2 of them (that is, two of the four might give solutions that are always imaginary for a given k.). The two that have real-valued solutions need to be considered carefully. You may have to give a solution that is conditional on the value of one or more variable.
Hint: if you use symbolic expressions, diff() and solve() are relevant.
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