1. y=x^10+1+root square (1-x),

p(0,2)

2. x^3-2x^2y+y^3-5=0,

p(1,2)

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1 Answer

  1. y=x¹⁰+x+√(1-x), dy/dx=10x⁹+1-1/(2√(1-x)). Put x=0: 1-½=½. Slope is ½ at point P(0,1). (P is on the curve because y=1 when x=0.)
  2. x³-2x²y+y³-5=0, 3x²-4xy-2x²dy/dx+3y²dy/dx=0. Put x=1, y=2: 3-8-2dy/dx+12dy/dx=0, -5+10dy/dx=0, 10dy/dx=5, dy/dx=½. Slope is ½ at point P(1,2). (P is on the curve because y=2 when x=1.)
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