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Increasing and Decreasing Functions — Maths STD 12 Science — Question

Maharashtra BoardEnglish MediumSTD 12 ScienceMathsIncreasing and Decreasing Functions3 Marks
Question
Show that $f(x) = e^{2x}$​​​​​​​ is increasing on $R$.
✓

Answer

$f(x) = e^{2x}$
$f'(x) = 2e^{2x}$
Now,
$\text{x}\in\text{R}$
Since the value of $e^{2x}​​​​​​​$​​​​​​​ is always positive for any real value of $x, e^{2x} > 0$.
$\Rightarrow 2e^{2x} > 0$
$\Rightarrow f'(x) > 0$
So, $f(x)$ is increasing on $R$.

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