Show that f(x) = e2x is increasing on R.

1.	Show that f(x) = e2x is increasing on R.
Answer» Given as f(x) = e^2x f'(x) = (d/dx)(e^2x) ⇒ f’(x) = 2e^2x For the function f(x) to be increasing, we must have ⇒ f’(x) > 0 ⇒ 2e^2x > 0 ⇒ e^2x > 0 Here, the value of e lies between 2 and 3 Therefore, whatever be the power of e (that is x in domain R) will be greater than zero. Hence, f(x) is increasing on interval R

Answer»

Given as f(x) = e^2x

f'(x) = (d/dx)(e^2x)

⇒ f’(x) = 2e^2x

For the function f(x) to be increasing, we must have

⇒ f’(x) > 0

⇒ 2e^2x > 0

⇒ e^2x > 0

Here, the value of e lies between 2 and 3

Therefore, whatever be the power of e (that is x in domain R) will be greater than zero.

Hence, f(x) is increasing on interval R

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