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Questions
Show that f(x) = e2x is increasing on R.
Show that the function given by f (x) = e 2x is increasing on R.
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Solution 1
\[f\left( x \right) = e^{2x} \]
\[f'\left( x \right) = 2 e^{2x} \]
\[\text { Now,} \]
\[x \in R\]
Since the value of `e^{2x}` text is always positive for any real value of x, ` e^{2x}` > 0 .
\[ \Rightarrow 2 e^{2x} > 0\]
\[ \Rightarrow f'\left( x \right) > 0\]
\[\text { So,f(x)is increasing on R} .\]
Solution 2
We have f(x) = e2x
f'(x) = 2e2x > 0, x `in` R
f is strictly increasing on R
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