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Implicit Differentiation

AP Calculus AB· difficulty 3/5

The tangent to x2+y2=25x^2 + y^2 = 25 at (3,4)(3, 4) is

  • A

    y=(3/4)x+4y = (3/4)x + 4

  • B

    y=−(3/4)x+25/4y = -(3/4)x + 25/4

  • C

    Both B and C

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  • D

    3x+4y=253x + 4y = 25

Explanation

Slope −3/4-3/4. y−4=−3/4(x−3)⇒y=−(3/4)x+25/4y - 4 = -3/4 (x - 3) \Rightarrow y = -(3/4)x + 25/4, equivalently 3x+4y=253x + 4y = 25.

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