2. a. max \( (\min ) 3 x y \) subject to \( x^{2}+y^{2}=8 \). b. \( \max (\min ) x+y \) subject to \( x^{2}+3 x y+3 y^{2}=3 \).
Added by Stephen C.
Close
Step 1
We need to find the maximum and minimum values of the function \(3xy\) subject to the constraint \(x^2 + y^2 = 8\). Show more…
Show all steps
Your feedback will help us improve your experience
Andrew Noble and 65 other Calculus 1 / AB educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
3. [Ch4 - Inequality-Const: 3] Minimize f(x,y) = x^2 + y^2 Subject to y >= x^2 + 1
Adi S.
Let $f(x, y)=x^{2}+3 y^{2} .$ Find the maximum and minimum values of $f$ subject to the given constraint (a) $x^{2}+y^{2}=1$ (b) $x^{2}+y^{2} \leq 1$
Higher-Order Derivatives; Maxima and Minima
Constrained Extrema and Lagrange Multipliers
Maximizing z = x · y by choices of x and y, subject to x + 2 · y = 12 (a). Form the Lagrangian and find the First-order conditions (b). Find x* and y* (c). Instead of using the Lagrangian, use the constraint to express y as a function of x and rewrite the objective function as a function of x, i.e., obtain z = f(x). By doing this, you have transformed the constrained optimization into an unconstrained one. Solve the problem and check whether it coincides with your answer in (b).
Madhur L.
Recommended Textbooks
Calculus: Early Transcendentals
Thomas Calculus
18,000,000+
Students on Numerade
Trusted by students at 8,000+ universities
Watch the video solution with this free unlock.
EMAIL
PASSWORD