Mean value theorem
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Khan AcademySal Khan
Mean value theorem
The Mean Value Theorem states that if a function f is continuous on the closed interval [a,b] and differentiable on the open interval (a,b), then there exists a point c in the interval (a,b) such that f'(c) is equal to the function's average rate of change over [a,b]. In other words, the graph has a tangent somewhere in (a,b) that is parallel ...
2014年1月13日
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cauchy mean value theorem bsc maths 1st year #Chauchy #theorems #bscmaths #youtubeshorts #maths
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Mean value theorem
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Mean value theorem
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2014年1月13日
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A Step-by-Step Guide on Using the Mean Value Theorem (Video)
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SOLVED:(a) Use the Mean-Value Theorem to show that if f is differentiable on an interval, and if |f^'(x)| ≤M for all values of x in the interval, then |f(x)-f(y)| ≤M|x-y| for all values of x and y in the interval. (b) Use the result in part (a) to show that |sinx-siny| ≤|x-y| for all real values of x and y .
SOLVED:(a) Use the Mean-Value Theorem to show that if f is differentiable on an interval, and if |f^'(x)| ≤M for all values of x in the interval, then |f(x)-f(y)| ≤M|x-y| for all values of x and y in the interval. (b) Use the result in part (a) to show that |sinx-siny| ≤|x-y| for all real values of x and y .
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