... to the limitations of the software, it cannot zoom in anymore to show properly labelled numbers. Failure The theory behind bisection is by splitting up two boundaries in two (by halves) so to defeat this method, there will need to be two roots within 1 unit (e.g. between 0 and 1) this way only one of the two roots can be found, and thus resulting in a failure. The chosen formula is shown below: f(x) = -12.4x4-0.3x3+9.9x2-0.6x-0.6 From this it can be seen that the bisection will fail (from theory) however the proof and calculations are below: Lower Bound Middle Value Upper Bound Lower Bound Middle Value Upper Bound -1.000000 -0.500000 0.000000 x -1.000000 -0.750000 -0.500000 x -2.200000 1.437500 -0.600000 f(x) -2.200000 1.621875 1.437500 f(x) Lower Bound Middle Value Upper Bound Lower Bound Middle Value Upper Bound -1.000000 -0.875000 -0.750000 x -1.000000 -0.937500 -0.875000 x -2.200000 0.437012 1.621875 f(x) -2.200000 -0.667841 0.437012 f(x) Lower Bound Middle Value Upper Bound Lower Bound Middle Value Upper Bound -0.937500 -0.906250 -0.875000 x -0.906250 -0.890625 -0.875000 x -0.667841 -0.066195 0.437012 f(x) -0.066195 0.197204 0.437012 f(x) Lower Bound Middle Value Upper Bound Lower Bound Middle Value Upper Bound -0.906250 -0.898438 -0.890625 x -0.906250 -0.902344 -0.898438 x -0.066195 0.068516 0.197204 f(x) -0.066195 0.001921 0.068516 f(x) As seen above, by using the bisection method, only one of the two roots is being zoomed into, meaning that it has failed in finding ...

See this essay or coursework document in full right now