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# Solution for Show that F(X) = (X − 1) Ex + 1 is an Increasing Function for All X > 0 ? - CBSE (Science) Class 12 - Mathematics

ConceptIncreasing and Decreasing Functions

#### Question

Show that f(x) = (x − 1) ex + 1 is an increasing function for all x > 0 ?

#### Solution

$f\left( x \right) = \left( x - 1 \right) e^x + 1$

$f'\left( x \right) = \left( x - 1 \right) e^x + e^x$

$= x e^x - e^x + e^x$

$= x e^x$

$\text { Given }:x > 0$

$\text { We know,}$

$e^x > 0$

$\Rightarrow x e^x > 0$

$\Rightarrow f'\left( x \right) > 0, \forall x > 0$

$\text { So },f(x)\text { is increasing on for all }x>0.$

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Solution Show that F(X) = (X − 1) Ex + 1 is an Increasing Function for All X > 0 ? Concept: Increasing and Decreasing Functions.
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