For the polynomial f(X)=2x^3-9x^2+11x-20
1 answer:
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Answer:
There is not root of the function on the interval [0, 1].
Step-by-step explanation:
The Intermediate Value Theorem says:
<em>If f(x) is a continuous function on [a, b], then for every d between f(a) and f(b), there exists a value c in between a and b such that f(c) = d.</em>
This means that whenever we can show that:
- there is a point above some line
- and a point below that line, and
- that the curve is continuous,
we can then safely say yes, there is a value somewhere in between that is on the line.
To show that there is solution between x = 0 and x = 1.
We evaluate the function at x = 0 and x = 1
We know that
at x = 0, the line is above zero and
at x = 1 the line is above zero.
We also know that the function is continuous but because the line is always above zero there is no solution at the interval (0, 1).
We can check our work with the graph of the function.
