Chinmayee patra Asked a Question
July 27, 2021 11:33 ampts 30 pts
4. (a) Let f: R" > Rbe a function whose partial derivative of order 2 are everywhere defined and continuous 6) Leta E R"be a critical point of f (i.e()= 0,i = 1,2,.n). Prove that a is local minimum of f provided that the Hessian matrix is positive definite at x =a. (i) Assume the Hessian matrix off is positive definite at all x. Prove that f has, at most, one critical point. (b) Evaluate -3xy)drdy whereR ((x.y) E R2 : (x+ 1) + y2 9,(x -1)2 + y 21)
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  • Alka gupta thankyou
    ans 4(b)...
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