Change of Sign Failure (Edexcel A-Level Mathematics): Flashcards

Conditions like repeated roots or discontinuities cause failure.

No sign change detected as function touches $x$-axis.

$f(x) = (x - 2)^2$ has a root at $x = 2$ without a sign change.

They may jump over roots, neglecting sign changes.

Newton-Raphson and fixed-point iteration may be more effective.

$f(x) = 1/x$ is undefined at $x = 0$, showing discontinuity.

No sign change detected even though roots exist in interval.

$f(a)$ and $f(b)$ both positive or both negative show no change.

It relies on continuity within the interval to detect roots.

Discontinuities prevent detection of root sign changes.