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calculus

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1. Let y = f(x) be the continuous function that satisfies the equation x^4-5x^2y^2+4y^4=0 and whose graph contains the points (2, 1) and (-2, -2). Let l be the line tangent to the graph of f at x = 2.
a. Find an expression for y’
b. Write an equation for line l

  • calculus - ,

    a. Differentiate implicitly.
    4x^3 -10x*y^2 -5x^2*2y*dy/dx +16y^3*dy/dx = 0
    4x^3 -10x*y^2 -10 x^2*y*dy/dx +16y^3*dy/dx = 0
    Plug in x = 2 and y = 1 to get dy/dx.
    4 -20 -40 dy/dx +16 dy/dx = 0
    -24 dy/dx = 16
    dy/dx = -2/3

    b. (y - 1)/(x-2) = -2/3

    Check my work.

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