Worksheet: Second- and Higher-Order Partial Derivatives

In this worksheet, we will practice finding the second- and higher-order derivatives of a multivariable function including mixed partial derivatives.


Consider the function 𝑓: given by the formula 𝑓(𝑥,𝑦)=𝑥+𝑦(𝑥+𝑦+1). Which of the statements below is incorrect?

  • A𝑓 has a minimum at the origin.
  • BThe third order partial derivatives satisfy the following equation 𝜕𝑓𝜕𝑥+𝜕𝑓𝜕𝑥𝜕𝑦+𝜕𝑓𝜕𝑥𝜕𝑦+𝜕𝑓𝜕𝑦=0.
  • C𝑓 is differentiable at the origin.
  • D𝑓 is continuous at the origin.

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