3. Iterate towards a maximum value of the function C(x, y) using the Newton's method with fixed step and the initial value [xo.Yo] = [3+ ¹255, 4-¹25] Present one iteration to solve [X₁. Y₁] including all hand calculations. Also, please present the function C(x,y) value for all iterations. Present [x₁, y₁] and C(x₁, y₁) with the accuracy of three significant numbers. 4.Iterate towards a minimum value of the function A(x) using the Golden Section algorithm. Use the initial gap of [-(525)-Calculate two iterations. Present all the observed values (also d), rejected values, values of function, and your best point. 5.. Iterate towards an extreme value of the function B(x) using the quadratic interpolation. Use the initial values x0 = -2.2- S/4, x₁ = 0, x₂ = 8. Calculate three iterations. Present all the observed values, rejected values and your best point. function: A(x) = 5 cos(($125)x)+ x B(x)=x2 +5+2x C(x,y) = -3x² +5x-(12-S)y²-2y +7xy

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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A(x), B(x) and C(x,y) are shown below and the value of s=7

3. Iterate towards a maximum value of the function C(x, y) using the Newton's method with fixed
step and the initial value [xo.Yo] = [3+ ¹255, 41255] Present one iteration to solve [X₁. Y₁]
including all hand calculations. Also, please present the function C(x,y) value for all iterations.
Present [x₁, y₁ ] and C(x₁, y₁) with the accuracy of three significant numbers.
4.Iterate towards a minimum value of the function A(x) using the Golden Section algorithm. Use
12
47
the initial gap of [-(525) - Calculate two iterations. Present all the observed values
S+25
(also d), rejected values, values of function, and your best point.
5.. Iterate towards an extreme value of the function B(x) using the quadratic interpolation. Use
the initial values x0 = -2.2- S/4, x₁ = 0, x₂ = 8. Calculate three iterations. Present all the
observed values, rejected values and your best point.
function:
A(x) = 5 cos((+25) x 7) + x
12
S+2
B(x)=ex/² + -X
C(x,y)=-3x² +5x-(12 S)y²-2y +7xy
Transcribed Image Text:3. Iterate towards a maximum value of the function C(x, y) using the Newton's method with fixed step and the initial value [xo.Yo] = [3+ ¹255, 41255] Present one iteration to solve [X₁. Y₁] including all hand calculations. Also, please present the function C(x,y) value for all iterations. Present [x₁, y₁ ] and C(x₁, y₁) with the accuracy of three significant numbers. 4.Iterate towards a minimum value of the function A(x) using the Golden Section algorithm. Use 12 47 the initial gap of [-(525) - Calculate two iterations. Present all the observed values S+25 (also d), rejected values, values of function, and your best point. 5.. Iterate towards an extreme value of the function B(x) using the quadratic interpolation. Use the initial values x0 = -2.2- S/4, x₁ = 0, x₂ = 8. Calculate three iterations. Present all the observed values, rejected values and your best point. function: A(x) = 5 cos((+25) x 7) + x 12 S+2 B(x)=ex/² + -X C(x,y)=-3x² +5x-(12 S)y²-2y +7xy
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