Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) §13.7 Constraints and Lagrange Multipliers, #30 · Multivariable Calculus · Lagrange multipliers

Minimize … subject to the inequality constraint

These problems allow inequality constraints, optional but good.

Minimize $f = x^{2} + y^{2}$ subject to the inequality constraint $x + y \geq 4$ . Now the minimum is at ______ and the multiplier is $λ =$ ______ and $f_{m i n} =$ ______. A small change to $4 + d k$ changes $f_{m i n}$ by what multiple of $d k$ ?

~11 minWritten answer · check your work with Lemma

Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) · §13.7 Constraints and Lagrange Multipliers, #30

Stuck? A gentle nudge

No hints for this one.

Something off?

Workspace

Your working

Check your full solution

Attach photos of your pages (up to 3) or one PDF — or check what you typed above. Lemma reads the work and verifies the reasoning, not just the answer.

Your first check today doesn't need an account.

Your photos and PDFs are read once and not stored — only the transcription is kept.