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MVT and IVT
2
AP Example
Thank you
Practice
Helpful Facts
- IVT is used to prove an intermediate y point, while MVT is used to prove an instantenous rate of change
- Another theorem called Rolle's Theorem states that if two points have a slope of zero, there must be a point in between that has a zero slope. (Just a derivation of MVT)
D
to satisfy IVT..
What is IVT?
Intermediate Value Theorem basically says that a continuous function cannot skip values.
Practice
f(x) is a continuous and differentiable function on the interval [-7,0],
and f(-7)=-3 while . What is the highest possible value for f(0)?
Solution:
Step 1: confirm that you can use MVT. See if the function is continuous and differentiable.
Step 2: f(0)- f(-7) = f'(x) (0-(-7))
Step 3:
Step 4: Finally, we need to plug in the highest value of f'(x), which is 2, in order to get the highest value of f(0)
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MVT and IVT
What is MVT?
MVT (Mean Value Theorem) states that a differentiable function has a point c whose instantaneous rate of change is equal to the average rate of change at (a,b) where a<c<b.
Gizem Cetin