Please include all math steps. Will leave good reviews if helped. No reposts pls.

Find all maxima and minima of f ( x ,y ) = ( x - 1 ) 2 + ( 9 - 2 ) over the region bounded by x2 ty 2 = 45. [Hint : Find all critical points in the interior of the domain first, then findF all local extrema on the boundary. consider using the method of Lagrunge multipliers for the latter part]