Find the value of x that maximizes the function f(x)=-2x^4 -4x^3 -16x^2 -10x for

Question

Find the value of x that maximizes the function f(x)=-2x^4 -4x^3 -16x^2 -10x for the range -2 less than or equal to x less than or equal to 1 (-2<x<1) using the golden section method, perform three iterations and calculate the approximate error at the end of each iteration Find the value of x that maximizes the function f(x)=-2x^4 -4x^3 -16x^2 -10x for the range -2 less than or equal to x less than or equal to 1 (-2<x<1) using the golden section method, perform three iterations and calculate the approximate error at the end of each iteration

Explanation / Answer

f(x)= -2x4-4x3-16x2-10x ; (-2<=x<=1)

f(-2) = -44

f(1) = -32

let x= -0.5 because it lies mid of -2 to 1

so, f(-0.5)= 1.375

1st iiteration

now let x =0 then f(0) = 0

now our x varies between -2 to 0 ,because f(-2) < f-(0.5) > f(0)

2nd iteration

now take x= -1,f(-1) = -4

now our x varies between -1 to 0, because f(-1) > f(-2)

3rditeration

now take x=-0.3, f(-0.3) = 1.651

now our x varies between -0.5 to 0,because f(-0.5) < f(0.3) > f(0)

4th iteration

take x= -0.4, f(-0.4) = 1.644

now our x varies between -0.4 to 0 because f(-0.5) < f(-0.4) >f(0)

by doing such a number of iteration such that x varies range size becomes tend to zero we find that x= -0.347 we get the maximum value of function.

error at 1st iteration = 0- (-0.347) = 0.347

error at 2nd iteration = -1-(-0.347) = -0.653

error at 3rd iteration = -0.3-(-0.347) = 0.047

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