How do you use the Intermediate Value Theorem to show that the polynomial function #x^3 - 2x^2 + 3x = 5# has a zero in the interval [1, 2]?
2 Answers
Here's one way to do it.
Explanation:
Let
(Needed because the intermediate value theorem is a theorem about functions .)
Observe that the equation
So the question now is to show that for at least one number
by the intermediate value theorem, there is at least one number
That is, the original equation has a solution.
Assuming you meant
Evaluate
Explanation:
Note:
That only leaves
Since