Question

Find all possible values of ‘a’ for which the function f(x) = e^2x – (a + 1) e^x + 2x is strictly increasing for all x in R.

Answer 1

Given f(x) = e^2x – (a + 1)e^x + 2x

⇒ f'(x) = 2e^2x – (a + 1)e^x + 2

= 2(e^x)² – (a + 1)e^x + 2

Since f is strictly increasing, so f'(x) > 0

Hence, the value of a is ∈ (–∞, 3)