.
A function f(x) = x3 + 2x - 1 has a zero within (0.1). Find the interval that the zero exists.
(A) (0.1, 0.3) (B) (0.4, 0.5) (C) (0.6, 0.7) (D) (0.7. 0.9)
~~~~~~~~~~~~
Notice that the given function is monotonic. It is clearly seen by an unarmed eye,
since it is the sum of two monotonic functions;
but also can be proved if you will take the derivative.
Since the function is monotonic, it has a UNIQUE zero inside interval (0,1).
It means, that in any given interval this function has the zero inside this interval if and only if
the values of the function at endpoints of the interval have opposite signs.
Having this said, the rest is a straightforward checking.
The answer is option (B).
Solved.
--------------
It is the way to determine the interval, containing the root, by computing the values of the given function ONLY,
without searching for the root itself.