Intermediate Value Theorem + Example on Proving a Root Exists

in MES Science2 years ago

In this video I go over what the intermediate value theorem is and show how it can be used to prove if a root of a function exists in any given interval.

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Intermediate Value Theorem: Plus an Example on Proving Roots of an Equation

Intermediate Value Theorem  Finding Roots.jpg

Intermediate Value Theorem:

Suppose that f is continuous on the closed interval [a, b] and let N be any number between f(a) and f(b), where f(a) ≠ f(b). Then there exists a number c in (a, b) such that f(c) = N.



Show that there is a root of the equation between x = 1 and x = 2:

4x3 – 6x2 + 3x – 2 = 0