(5) Let n > 1 be an integer. Consider f : Rn R defined by f(x ,xn) = z + + Find

Question

(5) Let n > 1 be an integer. Consider f : Rn R defined by f(x ,xn) = z + + Find the critical points of f (as with 2 or 3 variables, the critical points are those points (r,..., In) where the gradient of f is equal to zero). Does this give a local min, a local max, or a saddle point (use your intuition; we haven't yet developed a test). (6) Let n 1 be an integer. Consider f : Rn R defined by f(x1, ,xn) =-x Find the critical points off. Does this give a local min, a local max, or a saddle point (use your intuition; we haven't yet developed a test)

Explanation / Answer

(5) After findind the Cridical points

we will find the gradiant of gradiant that is f "

and we check for all critical points

if f '' of that critical point is >0 then at that point local min exist

and if f '' of that critical point is <0 then at that point local max exist

and if f '' =0 then may saddle point

(6) Same proceduce as (5)

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