Ex 5.8, 4 - Ex 5.8, 4
Verify Mean Value Theorem, if ๐‘“ (๐‘ฅ) = ๐‘ฅ2 – 4๐‘ฅ – 3 in the interval [๐‘Ž, ๐‘], where ๐‘Ž= - Ex 5.8

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  1. Chapter 5 Class 12 Continuity and Differentiability
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Ex 5.8, 4 Verify Mean Value Theorem, if ( ) = 2 4 3 in the interval [ , ], where = 1 = 4 ( ) = 2 4 3 , where a = 1 & b = 4 Mean Value Theorem satisfied if Condition 1 is continuous = 2 4 3 is a polynomial & Every polynomial function is continuous is continuous at [1, 4] Condition 2 If is differentiable = 2 4 3 is a polynomial & Every polynomial function is differentiable is differentiable at 1, 4 Condition 3 = 2 4 3 = 2 4 = 2 4 ( ) = (1) = 1 2 4 1 3 = 1 4 3 = 6 = 4 = 4 2 4 4 3 = 16 16 3 = 3 By Mean Value Theorem = = 3 6 4 1 = 3 + 6 3 = 3 3 = 1 2c 4 = 1 2c = 1 + 4 2c = 5 c = 5 2 Value of c = 5 2 which is lies between (1, 4) c = , Hence Mean Value Theorem satisfied

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