How to calculate maximum absolute error

If I have two solutions in following form

exact=x^(4)-x^(3) and app= (-2.220446049250313*10^(-16)) + (0.19676728660169784)* x + (4.6491983150099205)* x^(2) - (3.9010072748158082)* x^(3) + (2.3619056303875987)* x^(4) - (0.33198038154796344)* x^(5)

Then , how we can calculate maximum absolute error when x belongs to [0,2].

Answer 1

[Matt J]

The difference between two polynomials is a polynomial. Use calculus to find the maximum and minimum values of the difference polynomial.

[Nia Dutta]

It is diffucult to check every point of x.

[Matt J]

They are polynomials. It is an elementary calculus problem to find minima and maxima of polynomials using derivatives.