There are two square roots of 25. what is there only one sneer for the radius of the button.
2 answers:
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The Lagrangian for this function and the given constraints is
which has partial derivatives (set equal to 0) satisfying
This is a fairly standard linear system. Solving yields Lagrange multipliers of
and 
, and at the same time we find only one critical point at 
.
Check the Hessian for
, given by
is positive definite, since 
for any vector 
, which means 
attains a minimum value of 
at 
. There is no maximum over the given constraints.
which has partial derivatives (set equal to 0) satisfying
This is a fairly standard linear system. Solving yields Lagrange multipliers of
Check the Hessian for
check the picture below
and isosceles triangle, has two equal sides, thus, sides "a" and "b" for the triangle to be an isosceles, have to be equal
