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//Eg-12.1
//pg-507
clear
clc
x = 2.5;
h = 0.1;
deff('out = func(in)','out = in^3 -6*in^2 + 11*in -6')
//Forward Difference formulas
f(1) = (func(x+h) - func(x))/h;
f(2) = (-func(x+2*h)+4*func(x+h)-3*func(x))/(2*h);
//Backward Difference formulas
f(3) = (func(x)-func(x-h))/h;
f(4) = (3*func(x)-4*func(x-h)+func(x-2*h))/(2*h);
//Central Difference formulas
f(5) = (func(x+h)-f(x-h))/(2*h);
f(6) = (-func(x+2*h)+8*func(x+h)-8*func(x-h)+func(x-2*h))/(12*h);
printf('Value of derivative Type Order of error\n')
printf(' %f Forward 1\n',f(1))
printf(' %f Forward 2\n',f(2))
printf(' %f Backward 1\n',f(3))
printf(' %f Backward 2\n',f(4))
printf(' %f Central 2\n',f(5))
printf(' %f Central 4\n\n',f(6))
printf('The exact value is -0.25\nNote that the central difference formulas provide the best estimates of the derivative\n')
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