First slide

Mean value theorems

Question

$Rolle's theorem is applicable to function f (x) = \frac{\ln x}{x} over [a, b] where a, b are positive$ $integers, then the value of a + b$

Moderate

A

2
B

3
C

4
D

6

Solution

$\begin{array}{l} \frac{\ln a}{a} = \frac{\ln b}{b} \\ \frac{d y}{d x} = \frac{1 - \ln x}{x^{2}} \\ a = 2 \\ \Rightarrow b = 4 \\ As \frac{\ln 2}{2} = \frac{\ln 4}{4} \\ \Rightarrow a + b = 4 + 2 = 6 \end{array}$

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