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Increasing and Decreasing Functions — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsIncreasing and Decreasing Functions3 Marks
Question
Show that $f(x) = (x - 1)e^x + 1$ is an increasing function for all $x > 0.$
✓

Answer

$f(x) = (x - 1)e^x + 1$
$f'(x) = (x - 1)e^x + e^x= xe^x - e^x + e^x$
$= xe^x$
Given: $x > 0$
We know,
$e^x> 0$
$\Rightarrow xe^x > 0$
$\Rightarrow f'(x) > 0,$ for all $x > 0$
So, $f(x)$ is increasing on for all $x > 0.$

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