Implicit differentiation

Answer Key - Grade 12 Math Worksheet - Challenge Me

Circle the best answer, or write your answer on the line.

1. 1.

   On x² + y² = 5, dy/dx = −x/y. Ari differentiates again with the quotient rule. What is d²y/dx² at (1, 2)?

   -5/8
2. 2.

   On x² + y² = 10, dy/dx = −x/y. Bo differentiates again with the quotient rule. What is d²y/dx² at (1, -3)?

   10/27
3. 3.

   On x² + y² = 13, dy/dx = −x/y. Esme differentiates again with the quotient rule. What is d²y/dx² at (2, 3)?

   -13/27
4. 4.

   Kira differentiates x²y + y³ = 2 implicitly. What is dy/dx at (1, 1)?

   -1/2
5. 5.

   Luz differentiates x²y + y³ = 5 implicitly. What is dy/dx at (2, 1)?

   -4/7
6. 6.

   Milo differentiates x²y + y³ = -10 implicitly. What is dy/dx at (1, -2)?

   4/13
7. 7.

   Pia finds every point on x² + xy + y² = 3 where the tangent is horizontal. Which is right?

   • (1, −2) and (−1, 2)
   • (1, 2) and (−1, −2)
   • (1, −2)
   • (−2, 1) and (2, −1)
8. 8.

   Ren finds every point on x² + xy + y² = 12 where the tangent is horizontal. Which is right?

   • (−4, 2) and (4, −2)
   • (2, 4) and (−2, −4)
   • (2, −4)
   • (2, −4) and (−2, 4)
9. 9.

   Tala finds every point on x² − xy + y² = 3 where the tangent is horizontal. Which is right?

   • (1, −2) and (−1, 2)
   • (1, 2)
   • (2, 1) and (−2, −1)
   • (1, 2) and (−1, −2)
10. 10.

    Zee finds every point on x² − xy + y² = 27 where the tangent is horizontal. Which is right?

    • (3, 6) and (−3, −6)
    • (6, 3) and (−6, −3)
    • (3, 6)
    • (3, −6) and (−3, 6)