Rolle's theorem holds in [ 1 , 2 ] for the function f ( x ) = x 3 + b x 2 + c x at the point 3 4 . The values of b , c are respectively

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MathematicsApplication of DerivativeMonotonicity-Rolle's-theroemMedium2 minQB

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Rolle's theorem holds in $[1, 2]$ for the function $f (x) = x^{3} + b x^{2} + c x$ at the point $\frac{4}{3}$ . The values of $b, c$ are respectively

Answer:

Solution:

$f (1) = f (2)$ and $f^{'} (4/3) = 0$

$3 b + c = - 7 and 8 b + 3 c = - 16 b = - 5; c = 8$

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

⏱ 2mℹ️ Source: QB

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