Let fx y 3xx32y2y4on the domain D x y 5

Let f(x, y) = 3x-x^3-2y^2+y^4...on the domain D = {(x, y)| -5<=x<= 5, -2<=y <=2}.
Find greatest value for gradient

Solution

gradient = df/dx = 3-2x^2 ;
as x2 is always positive and the term is in -ve symbol;

gratesrt value occours at x= 0;

so highest value of gradient = 3

Let f(x, y) = 3x-x^3-2y^2+y^4...on the domain D = {(x, y)| -5<=x<= 5, -2<=y <=2}. Find greatest value for gradientSolutiongradient = df/dx = 3-2x^2

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