Find the critical points of the following functions.Use the Second Derivative Test to determine (if possible) whether each critical point corresponds to a local maximum, a local minimum,or a saddle point. If the Second Derivative Test is inconclusive,determine the behavior of the function at the critical points. f(x, y)=x2+y2−4x+5

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Find the critical points of the following functions.Use the Second Derivative Test to determine (if possible) whether each critical point corresponds to a local maximum, a local minimum,or a saddle point. If the Second Derivative Test is inconclusive,determine the behavior of the function at the critical points.  f(x, y)=x2+y2−4x+5

bahaistag · Accepted Answer

Step 1 The given function is, f(x, y)=x2+y2−4x+5 Apply the procedure for Maxima-Minima, Solve for critical points, ∂f∂x=0 ⇒−12f(2x−4)=0 ⇒x=2 ∂f∂x=0 ⇒−12f(2y)=9 ⇒y=0 Thus, (2, 0) is a critical point. Step 2 Solve for the second derivative as, ∂2f∂x2=∂∂x{(∂f∂x}) =∂∂x{(−12f(2x−4)}) =∂∂x{(1f(2−x)}) =f(−1)−(2−x){(−12f})(2x−4)f2 =1f2[−f+(2x−x)12f(2x−4)] =1f3[−f2+(2−x)(x−2)] =1f3[−(x2+y2−4x+5)−(x2+4−4x)] =1f3[−x2−y2+4x−5−x2−4+4x] =1f3[−2x2−x2+8x−9] Step 3 Substitute the values, r=∂2f∂x2Big∣(2, 0)

Find the critical points of the following functions.Use the Second

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