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Implicit Differentiation

AP Calculus AB· difficulty 3/5

For x2+y2=25x^2 + y^2 = 25, vertical tangents occur where the denominator of y′=−x/yy' = -x/y is zero, i.e. y=0y = 0. The points are

  • A

    (0,0)(0, 0)

  • B

    (±3,4)(\pm 3, 4)

  • C

    (0,±5)(0, \pm 5)

  • D

    (±5,0)(\pm 5, 0)

    check_circle

Explanation

y=0y = 0 on the circle gives x=±5x = \pm 5.

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