AI Tutor
Back to Optimization

Activity 11.10.3

Avg difficulty 2.5

For each of the functions given below:

  1. Find the critical points of the function
  2. Compute the discriminant DD and evaluate DD for each critical point.
  3. Use the Second Partial Derivatives Test to classify the critical points

  1. f(x,y)=3x3+y2−9x+4yf(x,y) = 3x^3+y^2-9x+4y

  2. f(x,y)=xy+2x+4yf(x,y) = xy + \frac{2}{x} + \frac{4}{y}

  3. f(x,y)=x3+y3−3xyf(x,y) = x^3 + y^3 - 3xy

Long, Keller & Schlicker, Active Calculus Multivariable, §11.10 Optimization, Activity 11.10.3

AI Tutor

Adapted from Active Calculus Multivariable © 2013–2026 Nicholas Long, Mitchel T. Keller, and Steven Schlicker. Licensed under CC BY-SA 4.0. Source: Active Calculus Multivariable. Imported at revision 692c03c.