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Mathematics - Application of Derivative Question with Solution | TestHub

MathematicsApplication of DerivativeMonotonicity-Rolle's-theroemEasy2 minQB

MathematicsEasysingle choice

A(1,0),B(e,1) are two points on the curve $y = lo g_{e} x$ . If P is a point on the curve at which the tangent to the curve is parallel to the chord AB, then, abscissa of P, is

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Answer:

Solution:

By LMVT, applied to $f (x) = lo g x$ on $[1, e], \exists an x_{0} \in (1, e) ∋ f^{1} (x_{0}) = \frac{f ( e ) - f ( 1 )}{e - 1}$

$\Rightarrow x_{0} = e - 1$

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

⏱ 2mℹ️ Source: QB

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