Mathematics - Application of Derivative Question with Solution | TestHub

MathematicsApplication of DerivativeMaxima-MinimaMedium2 minQB

MathematicsMediuminteger

Rolle's theorem holds for the function $f (x) = x^{3} + m x^{2} + n x$ on the interval $[1, 2]$ and the value of c is $\frac{4}{3}$ . Then $m + n =$

Answer:

Solution:

$f (1) = f (2) \Rightarrow 1 + m + n = 8 + 4 m + 2 n \Rightarrow 3 m + n + 7 = 0$ . $f^{1} (C) = 0 \Rightarrow 3 C^{2} + 2 m C + n = 0 \Rightarrow \frac{16}{3} + \frac{8 m}{3} + n = 0 (C = \frac{4}{3})$ $\Rightarrow 8 m + 3 n + 16 = 0$ on solving we get $m = - 5, n = 8$ Hence $m + n = 3$

Stream:JEESubject:MathematicsTopic:Application of DerivativeSubtopic:Maxima-Minima

⏱ 2mℹ️ Source: QB

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