Math CentralQuandaries & Queries


Question from sudhir, a student:

the equation of tangent of the curve (x/a)^n+(y/b)^n =2. at(a,b) is

Hi Sudhir,

Differentiate both sides of $(x/a)^n+(y/b)^n =2$ with respect to $x.$ The result will have a $y^\prime$ on the left side and 0 on the right side. Solve this expression for $y^\prime ,$ substitute $x = a$ and $y = b$ to find the slope of the curve at $(a, b)$ and then write the equation of the line through $(a, b)$ with this slope.


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