Explanation Given information: The function f ( x , y ) = 2 x − 6 y + 4 and the polygon is shown in Figure 22(A) Concept Used: A linear function f ( x , y ) = a x + b y + c has no critical point, therefore the global maximum and minimum value of must occur on the boundary of a bounded domain Calculation: As f ( x , y ) = 2 x − 6 y + 4 a linear function thus it has no critical point, therefore the global maximum and minimum value of must occur on the boundary of the polygon of Figure 22(A) As the polygon in figure 22(A) have boundary points ( − 3 , 0 ) , ( 1 , 0 ) , ( 0 , − 4 ) , ( 0 , 2 ) , checking value of function f ( x , y ) = 2 x − 6 y + 4 on boundary points f ( − 3 , 0 ) = 2

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Chapter 14.7, Problem 33E

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Find the global maximum and global minimum value of f(x,y)=2x−6y+4 on the polygon in Figure 22(A) and indicate where they occur

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Chapter 14.7, Problem 32E

Chapter 14.7, Problem 34E

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Taylor Series Approximation Example- H.W More terms used implies better approximation f(x) 4 f(x) Zero order f(x + 1) = f(x;) First order f(x; + 1) = f(x;) + f'(x;)h 1.0 Second order 0.5 True f(x + 1) = f(x) + f'(x)h + ƒ"(x;) h2 2! f(x+1) 0 x; = 0 x+1 = 1 x h f(x)=0.1x4-0.15x³- 0.5x2 -0.25x + 1.2 51 Taylor Series Approximation H.w: Smaller step size implies smaller error Errors f(x) + f(x,) Zero order f(x,+ 1) = f(x) First order 1.0 0.5 Reduced step size Second order True f(x + 1) = f(x) + f'(x)h f(x; + 1) = f(x) + f'(x)h + "(xi) h2 f(x,+1) O x₁ = 0 x+1=1 Using Taylor Series Expansion estimate f(1.35) with x0 =0.75 with 5 iterations (or & s= 5%) for f(x)=0.1x 0.15x³-0.5x²- 0.25x + 1.2 52

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Chapter 14 Solutions

CALCULUS 4E (HC) W/ ACHIEVE ACCESS

Ch. 14.1 - Prob. 1PQ Ch. 14.1 - Prob. 2PQ Ch. 14.1 - Prob. 3PQ Ch. 14.1 - Prob. 4PQ Ch. 14.1 - Prob. 5PQ Ch. 14.1 - Prob. 1E Ch. 14.1 - Prob. 2E Ch. 14.1 - Prob. 3E Ch. 14.1 - Prob. 4E Ch. 14.1 - Prob. 5E

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Find the global maximum and global minimum value of f ( x , y ) = 2 x − 6 y + 4 on the polygon in Figure 22(A) and indicate where they occur

Solution Summary: The author compares the global maximum and global minimum values of f(x,y)=2x-6y+4 and the polygon in Figure 22(A).

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Find the global maximum and global minimum value of f(x,y)=2x−6y+4 on the polygon in Figure 22(A) and indicate where they occur

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