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Posted 3 months ago
State a definition or a theorem in our class. (For example, what is the definition of continuous or what is mean value theorem?)


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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)f(x) be differentiable on the open interval (a,b)(a, b) and continuous on the closed interval [a,b][a, b]
step 3
Then the Mean Value Theorem guarantees that there exists at least one point cc in the interval (a,b)(a, b) such that the derivative of ff at cc is equal to the average rate of change of ff on [a,b][a, b]
step 4
Mathematically, this is expressed as f(c)=f(b)f(a)baf'(c) = \frac{f(b) - f(a)}{b - a}
The Mean Value Theorem states that for f(x)f(x) differentiable on (a,b)(a, b) and continuous on [a,b][a, b], there exists some c(a,b)c \in (a, b) such that f(c)=f(b)f(a)baf'(c) = \frac{f(b) - f(a)}{b - a}.
Key Concept
Mean Value Theorem
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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