Question

Find an interval of length 0.1 in [1, 2] containing a root of the equation x^7+4 x-10=0.

Answer 1

i wonder what we get if we divide it by x-1 and x-2

Answer 2

otherwise its just an interative process of your choosing

Answer 3

dividing doesnt seem to have any practical applications ... it was just a thought

Answer 4

newton had a method of taking the derivative and recaluclating

Answer 5

lol sorry i was thinking integrals for a second

Answer 6

the linear approximation of f(x) at c is: y - f(c) = f'(c) (x-c)

finding the x intercept gives us a new guess to play with \

xn = -f(c)/f'(c) + cf'(c)

Answer 7

when x_(n+1) - x_n <= .1/2 then we have found one of the endpoints of the interval

maybe doesnt need to be /2 ... but yeah