;BY FEBRUARY 27 YOUR ROOT FINDING MUST HANDLE THE FOLLOWING DIFFERENTIABLE FUNCTIONS...
;~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
2,1,-10,10,0.1				;CONTINUOUS, no roots 
sin(3),12,-10,10,0.1		;CONTINUOUS, no roots
x,3,-10,10,0.1				;CONTINUOUS, 1 root: {0.0} 
4*x-3,12,-10,10,0.1			;CONTINUOUS, 1 root: {0.75} 
x^2,-1,-10,10,0.1			;CONTINUOUS, 2 (equal) roots: {0.0} 
x^4-x^2,0,-5,5,0.1			;CONTINUOUS, 4 roots: {-1.0, 0.0, 1.0}
x^6,0,-9.95,9.95,0.1		;CONTINUOUS, 6 (equal) roots: {0.0}
sin(x),0,-7,7,0.1			;CONTINUOUS, 5 roots: {-6.28, -3.14, 0.0, 3.14, 6.28}
sin(x/2),0,-7,7,0.1			;CONTINUOUS, 3 roots: {-6.28, 0.0, 6.28}
cos(2*x),0,-7,7,0.1			;CONTINUOUS, 9 roots: {-5.5, -3.93, -2.36, -0.79, 0.79, 2.36, 3.93, 5.5, 7.07}