Mathematics - Application of Derivative Question with Solution | TestHub

MathematicsApplication of DerivativeMonotonicity-LMVTMedium2 minQB

MathematicsMediumsingle choice

The value of $c$ in the Lagrange's mean value theorem applied to the function $f (x) = x (x + 1) (x + 2)$ for $0 \leq x \leq 1$ is

Answer:

Solution:

$f^{1} (c) = 3 c^{2} + 6 c + 2 = \frac{f ( 1 ) - f ( 0 )}{1} = 6 \Rightarrow 3 c^{2} + 6 c - 4 = 0 \Rightarrow c = - 1 + \frac{21}{3} \in (0, 1)$

Stream:JEESubject:MathematicsTopic:Application of DerivativeSubtopic:Monotonicity-LMVT

⏱ 2mℹ️ Source: QB

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