Intermediate value theorem (IVT) review (article) | Khan Academy
If we have a function f (x) defined on an interval (a,b), if both lim (x->a+) f (x) and lim (x->b-) f (x) exist, then we should be able to make some conclusions about IVT being valid. Essentially, …
Intermediate value theorem (video) | Khan Academy
It was first proved by Bernard Bolzano, and there is in fact a slightly different formulation of IVT that is called Bolzano's theorem. That version states that if a continuous function is positive …
Worked example: using the intermediate value theorem (video
Discover how the Intermediate Value Theorem guarantees specific outcomes for continuous functions. With a given function f, where f(-2) = 3 and f(1) = 6, learn to identify the correct …
Justification with the intermediate value theorem: equation
The IVT only can be used when we know the function is continuous. If you are climbing a mountain, you know you must walk past the middle in order to get there, no matter how many …
Using the intermediate value theorem (practice) | Khan Academy
Use the Intermediate value theorem to solve some problems.
Justification with the intermediate value theorem: table
𝑓 (𝑥) = 0 could have a solution between 𝑥 = 4 and 𝑥 = 6, but we can't use the IVT to say that it definitely has a solution there.
Establishing continuity for EVT and IVT - Khan Academy
The intermediate value theorem (IVT) and the extreme value theorem (EVT) are existence theorems. They guarantee that a certain type of point exists on a graph under certain conditions.
Justification with the intermediate value theorem - Khan Academy
Given a table of values of a function, determine which conditions allow us to make certain conclusions based on the Intermediate Value Theorem or the Extreme Value Theorem.
Establishing differentiability for MVT (article) | Khan Academy
A function must be differentiable for the mean value theorem to apply. Learn why this is so, and how to make sure the theorem can be applied in the context of a problem.
AP®︎/College Calculus AB - Khan Academy
Learn AP®︎ Calculus AB—everything you need to know about limits, derivatives, and integrals to pass the AP® test.