12th grade Tangent lines using derivatives worksheet

Tangent lines using derivatives

Grade 12 Math Worksheet - Challenge Me

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

1. 1.

   Ari wants every x where the tangent to f(x) = x³ − 6x² is parallel to y = −9x + 2. List them, separated by commas.
2. 2.

   Bo wants every x where the tangent to f(x) = x³ − 3x² is parallel to y = 9x − 4. List them, separated by commas.
3. 3.

   Esme wants every x where the tangent to f(x) = x³ + 3x² is parallel to y = 24x + 1. List them, separated by commas.
4. 4.

   Jun wants every x where the tangent to f(x) = x³ − 9x² is parallel to y = −24x + 5. List them, separated by commas.
5. 5.

   Kira wants the line y = 6x − 1 to be tangent to f(x) = x² + c. What number c makes that happen?
6. 6.

   Luz wants the line y = 8x + 3 to be tangent to f(x) = x² + c. What number c makes that happen?
7. 7.

   Noah wants the line y = 12x − 5 to be tangent to f(x) = x² + c. What number c makes that happen?
8. 8.

   Pia finds the tangent line to f(x) = sin x at x = π. Which is it?

   • y = −x + π
   • y = x − π
   • y = −x − π
   • y = −x
9. 9.

   Ren finds the tangent line to f(x) = cos x at x = π/2. Which is it?

   • y = −x + π/2
   • y = x − π/2
   • y = −x
   • y = −x − π/2
10. 10.

    Zee finds the tangent line to f(x) = x ln x at x = e. Which is it?

    • y = 2x + 3e
    • y = 2x + e
    • y = 2x − e
    • y = ex + e − e²