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Implicit Differentiation

AP Calculus AB· difficulty 3/5

For y2−x3=0y^2 - x^3 = 0 (semi-cubical parabola), y′y' at (1,1)(1, 1) is

  • A

    23\tfrac{2}{3}

  • B

    12\tfrac{1}{2}

  • C

    13\tfrac{1}{3}

  • D

    32\tfrac{3}{2}

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Explanation

2yy′=3x2⇒y′=3x2/(2y)2y y' = 3x^2 \Rightarrow y' = 3x^2/(2y). At (1,1)(1, 1): 3/23/2.

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