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Next: 3.3.8 Example with a Linear Up: 3.3 Linear Interval Arithmetic Previous: 3.3.6 Monotonic Sections

3.3.7 Linear Functions

We will determine tex2html_wrap_inline35941 and tex2html_wrap_inline35701 for a linear function tex2html_wrap_inline34165 .

We have assumed that tex2html_wrap_inline35947 . Take any tex2html_wrap_inline35949 ; a simple proof by contradiction, which follows, shows that tex2html_wrap_inline34329 is an exact bound of g:

math18165

Assume there is a point tex2html_wrap_inline34333 such that tex2html_wrap_inline34335 . Let tex2html_wrap_inline34273 , so tex2html_wrap_inline35585 . Furthermore, tex2html_wrap_inline34251 and tex2html_wrap_inline35947 imply that tex2html_wrap_inline35627 .

figure18172

A quick review of the tex2html_wrap_inline35653 chart reveals this situation is impossible, since tex2html_wrap_inline35627 implies that tex2html_wrap_inline34301 . The tex2html_wrap_inline35653 chart predicts the sign of tex2html_wrap_inline35619 since tex2html_wrap_inline34273 .

next up previous notation contents
Next: 3.3.8 Example with a Linear Up: 3.3 Linear Interval Arithmetic Previous: 3.3.6 Monotonic Sections
Jeff TupperMarch 1996