## Related questions with answers

Question

Use Lagrange multipliers to find the maximum and minimum values of f subject to the given constraint, if such values exist.

$f\left(x_1, x_2\right)=x_1^2+x_2^2, \quad x_1+x_2=1$

Solution

VerifiedAnswered two weeks ago

Answered two weeks ago

Step 1

1 of 6Since $\text{grad } f = 2x \vec{i} + 2y\vec{j}$ and $\text{grad } g = \vec{i}+\vec{j},$ the Lagrange multiplier equation is given by

$2x \vec{i} + 2y\vec{j} = \lambda \vec{i}+\lambda \vec{j}$

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