Question

Separate the intervals in which the function f(x) = x − e^x is increasing or decreasing. 

Answer 1

f′(x) = 1 − e^x

Now, f′(x) > 0 ⇒ 1 − e^x > 0 ⇒ e^x < 1

⇒ x < 0 and f′(x) < 0 for all x > 0.

Therefore, f(x) is increasing in the interval (−∞, 0) and decreasing in the interval (0, ∞).