MCS 471 Floating Point Problem for Derivatives:

Newton's Quotient Approximation

Derivative example for

Function:   f(x) = 2*x,

Derivative:   f'(x) = 2,

Newton's Quotient Approximation:   Q_N= (2*(1+h)-2)/h,    h₂ > 0.

Floating Point Lesson:

The step h<\EM> should be small, BUT not too smallh<\EM>

and should not be as small as can be as in the Pure Calculus,

Else the derivative approxmation will ultimately be ZERO.