Question

Math

Posted 3 months ago

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State a definition or a theorem in our class. (For example, what is the definition of continuous or what is mean value theorem?)
Solution:
Do mean value therom
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Answer from Sia

Posted 3 months ago

Solution by Steps

step 1

The Mean Value Theorem is a fundamental theorem in calculus

step 2

The statement of the Mean Value Theorem is as follows: Let $f(x)$ be differentiable on the open interval $(a, b)$ and continuous on the closed interval $[a, b]$

step 3

Then the Mean Value Theorem guarantees that there exists at least one point $c$ in the interval $(a, b)$ such that the derivative of $f$ at $c$ is equal to the average rate of change of $f$ on $[a, b]$

step 4

Mathematically, this is expressed as $f'(c) = \frac{f(b) - f(a)}{b - a}$

Answer

The Mean Value Theorem states that for $f(x)$ differentiable on $(a, b)$ and continuous on $[a, b]$, there exists some $c \in (a, b)$ such that $f'(c) = \frac{f(b) - f(a)}{b - a}$.

Key Concept

Mean Value Theorem

Explanation

The Mean Value Theorem connects the average rate of change of a function over an interval to the instantaneous rate of change (derivative) at a specific point within that interval.

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