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Mean Value Theorems — MATHS STD 12 Science — Question

Rajasthan BoardEnglish MediumSTD 12 ScienceMATHSMean Value Theorems3 Marks
Question
State Lagrange's mean value theorem.
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Answer

Lagrange's Mean Value Theorem:
Let f(x) be a function defined on [a, b] such that
  1. It is continuous on [a, b] and
  2. It is differentiable on (a, b).
Then, there exists a real number $\text{c}\in(\text{a},\text{b})$ such that $\text{f}'(\text{c})=\frac{\text{f}(\text{b})-\text{f}(\text{a})}{\text{b}-\text{a}}.$

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