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Verify Lagrange’s mean value theorem for the function: and find the value of ‘c’ in the interval .

Mathematics20175 marksNumerical
Verify Lagrange’s mean value theorem for the function: $f(x) = x(1 - \log x)$ and find the value of ‘c’ in the interval $[1, 2]$.

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Continuity, Differentiability and Differentiation

From ISC 2017 Mathematics Paper 1, question 4(a).