Posted by terra on .
Show that tan^3(x)8(tan^2(x))+17(tan(x)08 = 0
has a root in [0.5, 0.6]. Apply the Bisection Method twice to find an interval of length 0.025 containing this root.
I have NO idea where to go with that equals 0 part...I could figure it without it but that throws me off completely..you can't plug any numbers in

calculus 
Steve,
If there is a root in [0.5,0.6] then that means that f(.5) * f(.6) < 0
That is, the graph crosses the axis there somewhere, and the function changes sign.
f(.5) = 0.9374
f(.6) = 0.2062
So, bisect the interval
f(.55) = 0.3539
Still negative, so bisect again
f(.575) = 0.0708
Still negative, so the root is in [0.575,0.6]
In fact, it turns out to be 0.5813