Question

Problem 1. [12 points; 4, 4, 4- Consider the function f(x,y) 1 2- (y-1)2 (i) Draw the level curve through the point P(1, 2). Find the gradient of f at the point P and draw the gradient vector on the level curve (ii) Draw the graph of f showing the level curve in (i) on the graph (iii) Explain why the function f admits a global minimum over the rectangle 0 x 2, y 1. Determine the minimum value and the point(s) where it occurs

Answer 1

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1- 1-x-y+24- 2 2- C O --2-1 0 2-2y0 Stationary Co, t) point 2-2 -2 tind minimum (en moximum 40 NOw ) ) -O minimun point 14 C- 0 value Minimum