Slope fields and checking a solution

Answer Key - Grade 12 Math Worksheet - Challenge Me

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

1. 1.

   Ari differentiates twice to check which function solves y″ + 4y = 0. Which one does?

   • y = 3 sin(4x)
   • y = 3 sin(2x)
   • y = e^(2x)
2. 2.

   Bo differentiates twice to check which function solves y″ − 9y = 0. Which one does?

   • y = 2e^(3x)
   • y = 2e^(9x)
   • y = 2 sin(3x)
3. 3.

   Jun differentiates twice to check which function solves y″ − 4y = 0. Which one does?

   • y = 5e^(−4x)
   • y = 5e^(−2x)
   • y = 5 cos(2x)
4. 4.

   On a solution curve of dy/dx = x² − y, Kira finds d²y/dx² at the point (3, 2). What is it?

   -1
5. 5.

   On a solution curve of dy/dx = x² − y, Luz finds d²y/dx² at the point (4, 5). What is it?

   -3
6. 6.

   On a solution curve of dy/dx = x² − y, Milo finds d²y/dx² at the point (−2, 1). What is it?

   -7
7. 7.

   dy/dx = y² − 6y + 5. Pia finds every constant solution y = c, a flat row in the slope field. List the c-values, separated by commas.

   1, 5
8. 8.

   dy/dx = y² − 5y. Ren finds every constant solution y = c, a flat row in the slope field. List the c-values, separated by commas.

   0, 5
9. 9.

   dy/dx = y² − 5y − 6. Tala finds every constant solution y = c, a flat row in the slope field. List the c-values, separated by commas.

   -1, 6
10. 10.

    dy/dx = y² − 2y − 8. Zee finds every constant solution y = c, a flat row in the slope field. List the c-values, separated by commas.

    -2, 4