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