Second derivative test

Exercise and reference answers

Questions

1. Statement is true

   Yes

   Statement

   A negative second derivative at a stationary point means a maximum

2. Statement is true

   Yes

   Statement

   3xe^(−x) differentiates to 3e^(−x)(1 − x)

3. Statement is true

   No

   Statement

   Setting dy/dx = 0 for 3xe^(−x) gives x = 0

4. Statement is true

   No

   Statement

   For partial derivatives you substitute the point before differentiating

5. Statement is true

   Yes

   Statement

   Differentiating p = x² + 2xy + 4xy² by x treats y as a constant

Instructions

Swipe true or false for each claim.