(a) Find f (x,y), f(x,y), f,(1,3), and f,(-2,4) for the given function. If
= f(x,y) = 3xy2 - x?y3 + 4x + 9
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Answer:fx =0 =⇒ x2 − xy − 4x =0 =⇒ x(x − y − 4)=0 =⇒ x = 0 or x − y − 4=0 fy =0 =⇒ x2 + ... ∇f = (2x − 2+2y,4y − 2+2x) = (0,0) =⇒ 2x − 2+2y = 4y − 2+2x =0 =⇒ y = 0,x = 1. However, the ... (3 + 2y2 − 4y)=0 =⇒ 4y − 4=0 =⇒ y = 1 with f(−1,1) = 1 . • the line x ... 2. ,1, 1. 2). Comparing with the vector we are given, we see that.
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