Let f : [ 0 , 4 ] → R , be a differentiable function. Then, there exists real numbers a , b ∈ ( 0 , 4 ) such that, ( f ( 4 ) ) 2 − ( f ( 0 ) ) 2 = Kf 1 ( a ) f ( b ) Where K, is

By LMVT, ∃ a ∈ ( 0 , 4 ) ∋ 4 − 0 f ( 4 ) − f ( 0 ) = f 1 ( a ) ⇒ f ( 4 ) − f ( 0 ) = 4 f 1 ( a )

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Mathematics - Application of Derivative Question with Solution | TestHub

MathematicsApplication of DerivativeMonotonicity-Rolle's-theroemMedium2 minQB

MathematicsMediumsingle choice

Let $f : [0, 4] \to R$ , be a differentiable function. Then, there exists real numbers $a, b \in (0, 4)$ such that, $(f (4))^{2} - (f (0))^{2} = Kf^{1} (a) f (b)$ Where K, is

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Solution:

By LMVT, $\exists a \in (0, 4) ∋ \frac{f ( 4 ) - f ( 0 )}{4 - 0} = f^{1} (a) \Rightarrow f (4) - f (0) = 4 f^{1} (a)$

Stream:JEESubject:MathematicsTopic:Application of DerivativeSubtopic:Monotonicity-Rolle's-theroem

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