Find the equation of the tangent and the normal to the following curves at the indicated points:

x2/3 + y2/3 = 2 at (1, 1)

finding the slope of the tangent by differentiating the curve




m(tangent) at (1,1) = – 1


normal is perpendicular to tangent so, m1m2 = – 1


m(normal) at (1,1) = 1


equation of tangent is given by y – y1 = m(tangent)(x – x1)


y – 1 = – 1(x – 1)


x + y = 2


equation of normal is given by y – y1 = m(normal)(x – x1)


y – 1 = 1(x – 1)


y = x


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