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# Solution for Show that F(X) = E1/X, X ≠ 0 is a Decreasing Function for All X ≠ 0 ? - CBSE (Science) Class 12 - Mathematics

ConceptIncreasing and Decreasing Functions

#### Question

Show that f(x) = e1/x, x ≠ 0 is a decreasing function for all x ≠ 0 ?

#### Solution

$f\left( x \right) = e^\frac{1}{x}$

$f'\left( x \right) = e^\frac{1}{x} \frac{d}{dx}\left( \frac{1}{x} \right)$

$= e^\frac{1}{x} \left( \frac{- 1}{x^2} \right)$

$= - \frac{e^\frac{1}{x}}{x^2}$

$\text { Here, }e^\frac{1}{x} > 0 \text { and } x^2 > 0, \text { for any real value of} x \neq 0.$

$\therefore f \left( x \right) = - \frac{e^\frac{1}{x}}{x^2} < 0, \forall x \in R, x \neq 0$

$\text { So,f(x) is a decreasing function }.$

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Solution for question: Show that F(X) = E1/X, X ≠ 0 is a Decreasing Function for All X ≠ 0 ? concept: Increasing and Decreasing Functions. For the courses CBSE (Science), CBSE (Commerce), CBSE (Arts), PUC Karnataka Science
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