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// example 4.31
// obtain the linear polinomial approximation to the function f(x)=x^3
// let P(x)=a0*x+a1
// hence I(a0,a1)= integral (x^3-(a0*x+a1))^2 in the interval [0,1]
printf('I=1/7-2*(a0/5+a1/4)+a0^2/3+a0*a1+a1^2')
printf('dI/da0 = -2/5+2/3*a0+a1=0')
printf('dI/da1 = -1/2+a0+2*a1=0')
// hence
printf('[2/3 1;1 2]*[a0 ;a1]=[2/5; 1/2]')
// solving for a0 and a1;
a0=9/10;
a1=-1/5;
// hence considering the polinomial with intercept P1(x)=(9*x-2)/10;
// considering the polinomial approximation through origin P2(x)=3*x/5;
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