• At the beginning the function is F: x → x^3−2, that I could study with this program,
for polynomial functions.
Alternatively, I can use pocket calculator directly.
function F(x) { with(Math) { /// you can change F [ now it is x - > x^3-2, ie pow(x,3)-2 ] return pow(x,3)-2 }}
We know that the solution is 21/3 = 1.259921049894873 . With the present script I find:
• Another example: we solve for x the equation sin(x) = x² - x + 1/2.
We can draw the graphs with JavaScript; for example, see the script fun00_equ.htm
function F(x) { with(Math) { return sin(x)-(x*x-x+1/2) }} a=0.29594100248899996 b=0.295941002489 ... a=0.28125 b=0.3125 a=0.25 b=0.3125 a=0.25 b=0.375 a=0.25 b=0.5 a=0 b=0.5 a=0 b=1 a=1.3521717451122257 b=1.352171745112226 ... a=1.34375 b=1.375 a=1.3125 b=1.375 a=1.25 b=1.375 a=1.25 b=1.5 a=1 b=1.5 a=1 b=2
2 solutions: 0.295941002489 1.352171745112