Calculus

Use implicit differentiation to find an equation of the tangent line to the curve at the given point x^2 + xy + y^2 = 3, (1,1)

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  1. 2x + y + xy' + 2yy' = 0
    You know x,y so just solve for y'.

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  2. differentiate x^2+xy+y^2
    f'= 2x+y+xy'+2yy'
    f' =2(1)+(1)+(1)y'+2(1)y'
    f'= 3+3y'
    -3=3y'
    y'=-1
    to find tangent line,
    y-y1=m(x-x1)
    y-1= -1(x-1)
    y-1= -x+1
    x+y= 1+1
    x+y=2
    answer: x+y=2

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