Question 1189314: 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)
Found 2 solutions by greenestamps, ikleyn:
Answer by greenestamps(13200)   (Show Source):
You can put this solution on YOUR website!
Graph the function with a graphing calculator or an online graphing utility to find the answer.
If you need to learn how to solve the problem using a specific method, re-post the question specifying the method. Then one of the tutors here can probably help you.
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Note to the student:
You responded by saying you need to solve the problem without a calculator.
You did not, as I told you to, specify HOW you need to solve the problem.
calculus?
Newton's method?
random trial and error?
trial and error with logical reasoning?
...?
Answer by ikleyn(52782)  (Show Source):
You can put this solution on YOUR website! .
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)
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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.
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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.
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