MATLAB: Difficult inequality to solve

inequality

abs((cos(x)+1/2*x^2)-1)*x^4)<=1/24, does anybody have any idea how to solve this on matlab or write down some possible codes?

Best Answer

since your function is even it is symmetric and it is monotone for x>0 or x<0

use fzero

>> f=@(x)((cos(x)+1./2.*x.^2)-1).*x.^4  - 1/24 % subtract the value to transform it into an issue of roots
>> solution=abs(fzero(f,0))
solution =
   1.0042
>> range=[-solution solution]
range =
   -1.0042    1.0042

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Best Answer

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